メイン＞研究室紹介＞後藤ゼミ＞業績等

業績等:後藤教授

I. 主要な研究業績

[1] 著書

• S. Goto and K. Nishida, The Cohen-Macaulay and Gorenstein properties of Rees algebras associated to filtrations, Mem. Amer. Math. Soc., 526 (1994)

[2] 論文

[1] S. Goto and K. Watanabe, On graded rings, I, J. Math. Soc. Japan, 30(1978), 179-213
[2] S. Goto, On Buchsbaum rings, J. Alg., 67(1980), 272-279
[3] S. Goto and Y. Shimoda, On the Rees algebras of Cohen-Macaulay local rings, Commutative algebra (Fairfax, Va., 1979), pp. 201-231, Lecture Notes in Pure and Appl. Math., 68, Dekker, New York, 1982
[4] S. Goto, On the associated graded rings of parameter ideals in Buchsbaum rings, J. Alg., 85(1983), 490-534
[5] S. Goto, Blowing-up of Buchsbaum rings, London Mathematical Society Lecture Note Series, 72(1983), 140-162
[6] D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Alg., 88(1984), 89-133
[7] S. Goto, K. Nishida, and K. Watanabe, Non-Cohen-Macaulay symbolic blow-ups for space monomial curves and counterexamples to Cowsik's question, Proc. Amer. Math. Soc., 120(1994), 383-392
[8] S. Goto, Y. Nakamura, and K. Nishida, Cohen-Macaulay graded rings associated to ideals, Amer. J. Math., 118(1996), 1197-1213
[9] S. Goto, Buchsbaumness in Rees algebras associated to ideals of minimal multiplicity, J. Alg., 213(1999), 604-661
[10] S. Goto, S. Iai, and K. Watanabe, Good ideals in Gorenstein local rings, Trans. Amer. Math. Soc. , 353(2001), 2309-2346
[11] S. Goto and Y. Nakamura, Multiplicity and tight closures of parameters, J. Alg., 244(2001), 302-311
[12] S. Goto and F. Hayasaka, Finite homological dimension and primes associated to integrally closed ideals, Proc. Amer. Math. Soc.,  130 (2002), 3159-3164
[13] S. Goto, Futoshi Hayasaka, and Satoe Kasuga, Towards a theory of Gorenstein m-primary integrally closed ideals, The proceedings of NATO Advanced Workshop, Sinaia (Romania), September 17-21, 2002
[14] S. Goto and Koji Nishida, Hilbert coefficients and Buchsbaumness of associated graded rings, J. Pure and Appl. Alg., 181(2003), 61-74
[15] S. Goto, F. Hayasaka, K. Kurano and Y. Nakamura, Rees algebras of the second syzygy module of the residue field of a regular local ring, Contemporary Mathematics (to appear)
他に論文85編
　
II. 研究内容の説明

後藤の研究成果は次の5課題に大別される。(1) Rees代数環構造論の創始[3]，(2) Buchsbaum環論の構築[5]，(3) イデアルの線型自由分解とCastelnuovo-Munford正則性に関する基礎研究[6], (4) Cowsik予想への反例構成[7], (5) Rees代数のCohen-Macaulay性判定法の確立[8]（引用文献番号は，研究業績（抜粋）内の論文番号である。）

論文[3]は下田保博(北里大・助教授)との共同研究であって，Rees環R(I)の環構造(Cohen-Macaulay性, Gorenstein性等)は，イデアル I の随伴次数環G(I)の環構造とそのa-不変量の言葉で完全に記述されることが示されている。この結果は (後にN. V. Trungと池田信によって大幅に拡張されたが) ，その後20年以上に渡り，Rees環研究の指針となった。Cohen-Macaulay環の拡張概念であるBuchsbaum環の理論構築は，W. Vogel, J. Stueckrad, N. V. Trung達との間で(協調的とはいえ), 激しい競争下に行われた。論文[5]には後藤の理論が最も端麗な形で集約されている。論文[6]はD. Eisenbudとの共同研究であり，Castelnuovo-Munford正則性に関する「Eisenbud-Goto予想」が提示された論文として名高い。論文[7]は西田康二（千葉大・助教授）・渡辺敬一（日大・教授）との共同研究である。symbolic Rees代数のNoether性に関するCowsik予想に歴史的な反例を提示した。この仕事は，標数0の世界の現象を正標数の世界に帰着させて解決した点でも，強く印象に残っている。随伴次数環G(I)のCohen-Macaulay性を判定する実際的方法の開発では，W. Vasconcelos, B. Ulrich, N. V. TrungやC. Huneke達，世界中の同業者との数年間に渡る激しい競争の中で，遂に他の追随を許さぬ成果を挙げるに至った[8]。この判定法も，Gorenstein性に関しては，改良の余地があり不満がないわけではないが，E. Hyryを始め後藤の学生の一人である居相真一郎（北海道教育大・専任講師）達によって継続され，優れた成果が挙がりつつあることは喜ばしい。Rees代数の環構造研究の内でも，arithmetic Cohen-Macaulay化の存在定理は，やはり後藤の学生の一人である川崎健（東京都立大学・助手）によって理想的な形に結実した。彼が用いた方法の中で最重要の部分は，後藤と山岸規久道（姫路独協大・教授）によって，共同研究の形で15年前に用意されていたことである。

最近は学生達と共に，BuchsbaumあるいはFLC局所環内のある種のm-準素イデアルの構造解析に従事している。興味深い理論が霧の中から次第に姿を現して来ることを大変嬉しく思っている。

III. 国際会議講演
計30回，主要なものは下記の通りである。
[1] 招待講演, Commutative Algebra : Durham, 1981年7月15-25日
[2] 招待講演, The 9-th International Symposium, Division of Mathematics of the Taniguchi Foundation, Conference on Commutative Algebra (堅田, 日本), 1981年9月3日-7日
[3] 招待講演, Microprogram on Commutative Algebra, MSRI (Berkeley, CA, 米国), 1987年6月15日7月2日
[4] 招待講演, Conference on Commutative Algebra and Combinatorics, 名古屋大学, 1990年8月15日-19日
[5] 招待講演 Commutative Algebra and Algebraic Geometry, Oberwolfach (ドイツ)，1992年5月2日-6日
[6] 招待講演, Syzygies, Multiplicities and Birational Algebra (Mount Holyoke College, South Hadley, MA, 米国), 1992年7月1日- 10日
[7] 招待講演, International Conference on Commutative Algebra, Vechta (ドイツ), 1994年7月27日-8 月1日
[8] 招待講演, Conference on Commutative Algebra to the Memory of Professor Hideyuki Matsumura, 名古屋大学, 1996年8月26日-28日
[9] 基調講演, Buchsbaum Varieties, A conference in honor of David Buchsbaum, (University of Catania, イタリア), 1998年4月26日-5月16日
[10] 招待講演, Commutative algebra, homological algebra and representation theory, A conference in honor of David Buchsbaum, (University of Genova, イタリア), 1998年5月24日-6月13日。
　2000年以降は，基調講演1回，招待講演10回を行っている。

IV. 国際会議主催
[1]  国際数学者会議 ICM 90 代数学分科会議長
[2] (D. Eisenbud, A. Ragusaと共催) Buchsbaum Varieties, A conference in honor of David Buchsbaum, Prat I, (University of Catania, イタリア), 1998年[3] (渡辺敬一と共催) Conference on Commutative Algebra in Japan, 2001, 2001年8月, 横浜

V. 学会誌等編集
[1] 日本数学会誌 Journal of the Mathematical Society of Japan 編集委員会委員 (1994-1997)
[2] 日本数学会誌 Journal of the Mathematical Society of Japan 編集委員会委員長 (1997-1999)
[3] Beitraege zur Algebra und Geometrie 編集委員会委員 (1997-現在に至る)

○2000年-2005年の間だけの研究業績を纏めると下記の通りである。
I. 国際会議講演
2000年
[1] Good ideals in Gorenstein local rings and related topics, Conference on Commutative Algebra, Algebraic Geometry, and Singularity Theory, A tribute to Manfred Herrmann, Max Plank Institut fuer Mathematik, Bonn (ドイツ), 2000年6月2日-3日
[2] Complete intersection in overrings of a certain one-dimensional Gorenstein graded local ring, International Conference on Commutative Algebra and Algebraic Geometry, CIRM, Luminy (フランス), 2000年6月5日-9日

2001年
[1] The a-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings, Conference on Commutative Algebra 2001, 横浜（日本），2001年8月20日-25日

2002年
[1] Finite homological dimension and primes associated to integrally closed ideals, Current trends in Commutative Algebra, Levico (Trent, Italy), June 17-21, 2002
[2] Towards a theory of Gorenstein m-primary integrally closed ideals, NATO Advanced Research Workshop : Commutative Algebra, Singularities and Computer Algebra, Sinaia (Romania), September 17-22, 2002

2003年
[1] The equality I^2 = QI in Buchsbaum local rings, Commutative algebra and its interaction with algebraic geometry, CIRM in Luminy (France), June 2-6, 2003
[2] The equality I^2 = QI in Buchsbaum rings, Lisbon Conference on Commutative Algebra, Lisbon (Portugal), June 23-27, 2003

2004年
[1] On the associated graded rings of certain m-primary ideals in a generalized Cohen-Macaulay local ring，Commutative Algebra and Algebraic Geometry in honor of Professor Masayoshi Miyanishi on the occasion of his retirement, Toyonaka Campus, Osaka University (Osaka, Japan), March 1-5, 2004
[2] The equality $I^2 = QI$ in FLC local rings, The International Workshop on Commutative Algebra and its Interaction to  Algebraic Geometry and Combinatorics, The Abdus Salam International Center for Theoretical Physics (Trieste, Italy),  May 24-June 11, 2004
[3] Noether安定局所環の構造，Conference on Commutative Algebra and Algebraic Geometry for the memory of Tetsushi Ogoma, Kochi University (Kochi, Japan), August 4-6, 2004
[4] Stable local rings, The BIRS workshop, Commutative Algebra : Homological and Birational Theory Dates, Banff International Research Station (Banff, Canada), September 11 - 16, 2004

II. 発表論文
2000年
[1] S. Goto and S. Iai, Embeddings of certain graded rings into their canonical modules, J. Alg.，228(2000), 377-396
[2] S. Goto, Cohen-Macaulayness versus negativity of a-invariants in Rees algebras associated to ideals of minimal multiplicity, J. Pure and Applied Alg., 152(2000), 93-107
[3]  S. Goto, S. Haraikawa, and S. Iai, Complete intersection in overrings of a certain one-dimensional Gorenstein graded local ring, J. Alg., 233(2000), 772-790

2001年
[1] S. Goto, S. Iai, and K. Watanabe, Good ideals in Gorenstein local rings, Trans. Amer. Math. Soc. , 353(2001), 2309-2346
[2] S. Goto and K. Nishida, Finite modules of finite injective dimension over a Noetherian algebra, J. London Math. Soc., (2), 63(2001), 319-335
[3] D. Aghcheghloo, R. Enshaei, S. Goto, and R. Y. Sharp, Comparison of multigraded and ungraded Cousin complexes, Proc. Edinburgh Math. Soc., 44(2001) 365-378
[4] S. Goto and Y. Nakamura, Multiplicity and tight closures of parameters, J. Alg., 244(2001), 302-311

2002年
[1] S. Goto and K. Nishida, Towards a theory of Bass numbers with application to Gorenstein algebras, Colloquium Mathematicum, 91 (2002), 191-253
[2] S. Goto and M. Kim, Equimultiple good ideals, J. Math. Kyoto Univ., 42-1(2002), 21-32
[3] S. Goto, S. Iai, and M. Kim, Good ideals in Gorenstein local rings obtained by idealization, Proc. Amer. Math. Soc., 130(2002), 337-344
[4] S. Goto and Y. Nakamura, The bound of the difference between parameter ideals and their tight closures, Tokyo J. Math., 25-1(2002), 41-48
[5] S. Goto and S. Iai, Gorenstein associated graded rings of analytic deviation two ideals,  J. Alg., 248(2002), 708-723
[6] S. Goto and F. Hayasaka, Finite homological dimension and primes associated to integrally closed ideals, Proc. Amer. Math. Soc., 130(2002), 3159-3164
[7] S. Goto and F. Hayasaka, Finite homological dimension and primes associated to integrally closed ideals II, J. Math. Kyoto Univ., 42-4(2002), 631-639
[8] S. Goto and S. Haraikawa, Good ideals in Artinian Gorenstein local rings obtained by idealization, Tokyo J. Math., 25-2(December, 2002), 493-49

2003年
[1] S. Goto, F. Hayasaka and S. Iai, The a-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings, Proc. Amer. Math. Soc. , 131(2003), 87"94
[2] S. Goto and K. Nishida, Hilbert coefficients and Buchsbaumness of associated graded rings, J. Pure and Appl. Alg., 181(2003), 61-74
[3] S. Goto, F. Hayasaka, and S. Kasuga, Towards a theory of Gorenstein m-primary integrally closed ideals, J. Herzog and V. Vuletescu (eds.), Commutative Algebra, Singularities and Computer Algebra, 159-177; The Proceedings of NATO Advanced Research Workshop : Sinaia (Romania), September 17-22, 2002
[4] S. Goto and H. Sakurai, The equality $I^2 = QI$ in Buchsbaum rings, Rendiconti del Seminario Matematico dell'Universit di Padova, 110(2003), 25-56
[5] S. Goto and Y. Shimoda, Parametric decomposition of powers of ideals versus regularity of sequences, Proc. Amer. Math. Soc., 132-4(2003), 929-933
[6] S. Goto and Y. Shimoda, On the parametric decomposition of powers of parameter ideals in a Noetherian local ring, Tokyo J. Math., 27-1(2004), 125-135

2004年
[1] S. Goto and H. Sakurai, The reduction exponent of socle ideals associated to parameter ideals in a Buchsbaum local ring of multiplicity two, J. Math. Soc. Japan, 56(2004), 1157-1168
[2] S. Goto, F. Hayasaka, K. Kurano, and Y. Nakamura, Rees algebras of the second syzygy module of the residue field of a regular local ring, Contem. Math. (to appear)
[3] S. Goto and S. Iai, Gorenstein graded rings associated to ideals, CRM Preprint No. 540, May, 2003

2005年
[1] S. Goto and H. Sakurai, When does the equality $I^2 = QI$ hold true in Buchsbaum rings ?, the Special Volume on 'Commutative Algebra with a focus on geometric and homological aspects', Proceedings of Sevilla, June 18-21, 2003 and Lisbon, June 23-27, 2003 to appear in Marcel Dekker's Lecture Notes in Pure and Applied Mathematics Series, 244(2005), 115-139
[2] S. Goto and S. Iai, Gorenstein graded rings associated ideals , J. Algebra, 294(2005), 373-407
[3] S. Goto, W. Heinzer, and Mee-Kyoung Kim, The leading ideal of a complete intersection of height two, J. Algebra (to appear)

○最近5年間に交付を受けた研究費
後藤が最近5年間に交付を受けた研究費等は下記の通りである。（金額の単位は千円である。）

[1] 文部省科学研究費基盤研究C(2)，研究期間：平成9-10，研究題目：「Rees代数の環構造」，代表者：後藤四郎，研究費の総額：5,000　
[2] 文部省科学研究費基盤研究C(2)，研究期間：平成11-12，研究題目：「可換環論・特にBlow-up ringsのBuchsbaum性の研究」，代表者：後藤四郎，研究費の総額：[3] 文部省科学研究費基盤研究C(2)，研究期間：平成13-15，研究題目：「Blow-up ringsの環構造の研究」，代表者：後藤四郎，研究費の総額：5,000
[3] 文部省科学研究費基盤研究C(2)，研究期間：平成13-15，研究題目：「Blow-up ringsの環構造の研究」，代表者：後藤四郎，研究費の総額：5,000
[4] 明治大学科学技術研究所重点研究費，平成13-14，研究題目：「可換環論と関連分野の総合的研究」，代表者：後藤四郎，研究費の総額：2,175　
[5] 文部省科学研究費基盤研究C(2)，研究期間：平成16-18，研究題目：「イデアルと加群に随伴する次数代数の環構造研究」，代表者：後藤四郎，研究費の総額：5,000

○付録
I. 後藤四郎全研究業績
(1) 著書
[1] S. Goto and K. Nishida, The Cohen-Macaulay and Gorenstein properties of Rees algebras associated to filtrations, Mem. Amer. Math. Soc., 526 (1994)

(2) 学術論文
[1] S. Goto, On modules without q-torsion, the Science Reports of the Tokyo Kyouiku Daigaku, Section A, 11(1972), 139-142
[2] S. Goto, Note on the existence of Gorenstein modules, the Science Reports of the Tokyo Kyouiku Daigaku, Section A, 12(1973), 33-35
[3] S. Goto, When do the determinantal ideals define Gorenstein rings?, the Science Reports of the Tokyo Kyouiku Daigaku, Section A, 12(1974), 129-145
[4] Y. Aoyam and S. Goto, On the type of graded Cohen-Macaulay rings, J. Math. Kyoto Univ., 15(1975), 19-23
[5] S. Goto, The Veronesean subrings of Gorenstein rings, J. Math. Kyoto Univ., 16(1976), 51-55
[6] S. Goto, N. Suzuki, and K. Watanabe, On affine semigroup rings, Japan. J. Math., 2(1976), 1-12
[7] S. Goto, The divisor class group of a certain Krull domain, J. Math. Kyoto Univ., 17(1977), 47-50
[8] S. Goto and S. Tachibana, A complex associated with a symmetric matrix, J. Math. Kyoto Univ., 17(1977), 51-54
[9] S. Goto, A problem on Noetherian local rings of characteristic p, Proc. Amer. Math. Soc., 64(1977), 199-205
[10] S. Goto and K. Watanabe, The structure of one dimensional F-pure rings, J. Alg., 49(1977), 415-421
1[1] S. Goto and K. Watanabe, On graded rings, I, J. Math. Soc. Japan, 30(1978), 179-213
[12] S. Goto, Invariant subrings under the action by a finite group generated by pseudo-reflections, Osaka J. Math., 15(1978), 47-50
[13] S. Goto, The rank of syzygies under the action by a finite group, Nagoya Math. J., 71(1978), 1-12
[14] S. Goto and K. Watanabe, On Graded rings, II, Tokyo J. Math., 1(1978), 237-261
[15] S. Goto, On the Gorensteinness of the determinantal loci, J. Math. Kyoto Univ., 19(1979), 371-374
[16] S. Goto, Gorenstein環について (in Japanese), 「数学」（岩波書店）, 31(1979), 349-364
[17] S. Goto and Y. Shimoda, On Rees algebras over Buchsbaum rings, J. Math. Kyoto Univ., 20(1980), 691-708
[18] S. Goto, On the Cohen-Macaulayfication of certain Buchsbaum rings, Nagoya Math. J., 80(1980), 107-116
[19] S. Goto, On Buchsbaum rings, J. Alg., 67(1980), 272-279
[20] S. Goto, On Buchsbaum rings obtained by gluing, Nagoya Math. J., 83(1981), 123-135
[21] S. Goto, Rings with linear resolution, the Proceedings of the 9-th International Symposium, Division of Mathematics of the Taniguchi Foundation, Conference on Commutative Algebra (Katata, September 3-7, 1981), 1981, 4-11
[22] S. Goto, Buchsbaum rings with multiplicity 2, J. Alg., 74(1982), 494-508
[23] S. Goto, Approximately Cohen-Macaulay rings, J. Alg., 76(1982), 214-225
[24] Goto, Buchsbaum rings of maximal embedding dimension, J. Alg., 76(1982), 383-399
[25] S. Goto, Vanishing of \roman{Ext}_A^t(M,A), J. Math. Kyoto Univ., 22(1982), 481-484
[26] S. Goto and Y. Shimoda, On the Rees algebras of Cohen-Macaulay local rings, Lecture Notes in Pure and Applied Mathematics, 68(1982), 201-231, Marcel Dekker
[27] S. Goto, Every Noetherian uniformly coherent ring has dimension at most 2, J. Math. Kyoto Univ., 23(1983), 269-279
[28] S. Goto and K. Yamagishi, Finite generation of Noetherian graded rings, Proc. Amer. Math. Soc., 89(1983), 41-44
[29] S. Goto and T. Ogawa, A note on rings of finite local cohomology, Tokyo J. Math., 6(1983), 403-411
[30] S. Goto and Y. Shimoda, On the Gorensteinness of Rees and form rings of almost complete intersections, Nagoya Math. J., 92(1983), 69-88
[31] S. Goto, On the associated graded rings of parameter ideals in Buchsbaum rings, J. Alg., 85(1983), 490-534
[32] S. Goto, Blowing-up of Buchsbaum rings, London Mathematical Society Lecture Note Series, 72(1983), 140-162
[33] S. Goto, Noetherian local rings with Buchsbaum associated graded rings, J. Alg., 86(1984), 336-384
[34] S. Goto and N. Suzuki, Index of reducibility of parameter ideals in a local ring, J. Alg., 87(1984), 53-88
[35] S. Goto, A note on quasi-Buchsbaum rings, Proc. Amer. Math. Soc., 90(1984), 511-516
[36] D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Alg., 88(1984), 89-133
[37] Y. Aoyam and S. Goto, On the endmorphism ring of a canonical module, J. Math. Kyoto Univ., 25(1985), 21-30
[38] Y. Aoyam and S. Goto, A brief summary of the elements of the theory of dualizing complexes and Sharp's conjecture, The Curves Seminar at Queen's (Vol. 4), Queen's Papers in Pure and Applied Mathematics, 76(1986)
[39] Y. Aoyam and S. Goto, Some special cases of a conjecture of Sharp, J. Math. Kyoto Univ., 26(1986), 613-634
[40] S. Goto, Integral closedness of complete-intersection ideals, J. Alg., 108(1987), 151-160
[41] S. Goto, Maximal Buchsbaum modules over regular local rings and a structure theorem for generalized Cohen-Macaulay modules, Advanced Studies in Pure Mathematics; Commutative Algebra and Combinatorics, 11(1987), 39-64
[42] Y. Aoyam and S. Goto, a conjecture of Sharp-the case of local  rings with \roman{dim} non CM \leq 1 or \roman{dim} \leq 5, Algebraic Geometry in honor of Masayoshi Nagata, 1987, 27-34
[43] S. Goto and K. Nishida, Rings with only finitely many isomorphism classes of indecomposable maximal Buchsbaum modules, J. Math. Soc. Japan, 40(1988), 501-518
[44] S. Goto, Surface singularities of finite Buchsbaum representation type, Commutative Algebra, Mathematical Sciences Research Institute Publications, 15(1989), 247-263
[45] S. Goto, On the surjectivity criterion for Buchsbaum modules, Proc. Amer. Math. Soc., 108(1990), 641-646
[46] S. Goto, M. Herrmann, K. Nishida, and O. Villamayor, On the structure of Noetherian symbolic Rees algebras, manuscripta mathematica, 67(1990), 197-225
[47] S. Goto and N. Suzuki, What makes \roman{Tor}_1^R(R/I,I) free?, Proc. Amer. Math. Soc., 112(1991), 605-611
[48] S. Goto, K. Nishida, and Y. Shimoda, The Gorensteinness of the symbolic Rees algebras for space curves, J. Math. Soc. Japan., 43(1991), 465-481
[49] S. Goto, K. Nishida, and Y. Shimoda, Topics on symbolic Rees algebras for space monomial curves, Nagoya Math. J. 124(1991), 99-132
[50] M. Morimoto and S. Goto, Non-Cohen-Macaulay symbolic blow-ups for space monomial curves, Proc. Amer. Math. Soc., 116(1992), 305-311
[51] S. Goto, K. Nishida, and Y. Shimoda, The Gorensteinness of the symbolic blow-ups for certain space monomial curves, Trans. Amer. Math. Soc., 340(1993), 323-335
[52] S. Goto, Curve singularities of finite Buchsbaum representation type, J. Alg., 163(1994), 447-480
[53] S. Goto, K. Nishida, and K. Watanabe, Non-Cohen-Macaulay symbolic blow-ups for space monomial curves and counterexamples to Cowsik's question, Proc. Amer. Math. Soc., 120(1994), 383-392
[54] S. Goto and S. Huckaba, On graded rings associated to analytic deviation one ideals, Amer. J. Math., 116(1994), 905-919
[55] S. Goto and Y. Nakamura, On the Gorensteinness of graded rings associated to ideals of analytic deviation one, Contemporary Mathematics, 159(1994), 51-72
[56] S. Goto, Prime ideals of height two whose associated graded rings are Gorenstein integral domains-an extension of Huckaba and Huneke's examples, Comm. Alg., 22(1994), 857-864
[57] S. Goto and Y. Nakamura, Cohen-Macaulay Rees algebras of ideals having analytic deviation two, Tohoku J. Math., 46(1994), 573-586
[58] S. Goto and Y. Nakamura, Gorenstein graded rings associated to ideals of analytic deviation two, J. Alg., 175(1995), 811-819
[59] S. Goto, Y. Nakamura, and K. Nishida, Cohen-Macaulayness in graded rings associated to ideals, J. Math. Kyoto Univ., 36(1996), 229-250
[60] S. Goto, Y. Nakamura, and K. Nishida, Cohen-Macaulay graded rings associated to ideals, Amer. J. Math., 118(1996), 1197-1213
[61] S. Goto, Y. Nakamura, and K. Nishida, On the Gorensteinness in graded rings associated to certain ideals of analytic deviation one, Japan. J. Math., 23(1997), 303-318
[62] J. Yoshida and S. Goto, On graded rings associated to local algebras with global dimension two, Mem. Inst. Sci. Tech. Meiji Univ., 36(1997), 113-120
[63] S. Goto, Buchsbaumness in Rees algebras associated to ideals of minimal multiplicity, J. Alg., 213(1999), 604-661
[64] S. Goto and K. Nishida, Catenarity in module finite algebras, Proc. Amer. Math. Soc., 127 (1999), 3495-3502
[65] S. Goto and K. Nishida, Minimal injective resolutions of  Cohen-Macaulay isolated singularities, Arch. Math. 73 (1999), 249-255
[66] S. Haraikawa and S. Goto, イデアル化によって得られたArtin Gorenstein局所環内のgood idealsの構造と分布について (in Japanese), 明治大学科学技術研究所紀要 38 (1999), 9-24
[67] S. Goto and S. Iai, Embeddings of certain graded rings into their canonical modules, J. Alg.，228(2000), 377-396
[68] S. Goto, Cohen-Macaulayness versus negativity of a-invariants in Rees algebras associated to ideals of minimal multiplicity, J. Pure and Applied Alg., 152(2000), 93-107
[69]  S. Goto, S. Haraikawa, and S. Iai, Complete intersection in overrings of a certain one-dimensional Gorenstein graded local ring, J. Alg., 233(2000), 772-790
[70] S. Goto, S. Iai, and K. Watanabe, Good ideals in Gorenstein local rings, Trans. Amer. Math. Soc. , 353(2001), 2309-2346
[71] S. Goto and K. Nishida, Finite modules of finite injective dimension over a Noetherian algebra, J. London Math. Soc., (2), 63(2001), 319-335
[72] D. Aghcheghloo, R. Enshaei, S. Goto, and R. Y. Sharp, Comparison of multigraded and ungraded Cousin complexes, Proc. Edinburgh Math. Soc., 44(2001) 365-378
[73] S. Kasuga, S. Goto, and F. Hayasaka, 1次元Noether局所環内の整閉なGorenstein m-準素イデアルの構造と分布について,  明治大学理工学部研究報告，24(2000), 21-29
[74] S. Goto and F. Hayasaka, 射影次元有限の整閉イデアルに付随する素イデアルの講造,  明治大学理工学部研究報告，25(2001), 25-27
[75] S. Goto and Y. Nakamura, Multiplicity and tight closures of parameters, J. Alg., 244(2001), 302-311
[76] S. Goto and K. Nishida, Towards a theory of Bass numbers with application to Gorenstein algebras, Colloquium Mathematicum, 91 (2002), 191-253
[77] S. Goto and M. Kim, Equimultiple good ideals, J. Math. Kyoto Univ., 42-1(2002), 21-32
[78] S. Goto, S. Iai, and M. Kim, Good ideals in Gorenstein local rings obtained by idealization, Proc. Amer. Math. Soc., 130(2002), 337-344
[79] S. Goto and Y. Nakamura, The bound of the difference between parameter ideals and their tight closures, Tokyo J. Math., 25-1(2002), 41-48
[80] S. Goto and S. Iai, Gorenstein associated graded rings of analytic deviation two ideals,   J. Alg., 248(2002), 708-723
[81] S. Goto and F. Hayasaka, Finite homological dimension and primes associated to integrally closed ideals, Proc. Amer. Math. Soc., 130(2002), 3159-3164
[82] S. Goto and F. Hayasaka, Finite homological dimension and primes associated to integrally closed ideals II, J. Math. Kyoto Univ., 42-4(2002), 631-639
[83] S. Goto and S. Haraikawa, Good ideals in Artinian Gorenstein local rings obtained by idealization, Tokyo J. Math., 25(2002), 493-499
[84] 櫻井秀人・後藤四郎，いつ等式I^2=QIが成り立つか？，明治大学理工学部研究報告，26-82(2002), 19-22
[85] 櫻井秀人・後藤四郎，重複度2のBuchsbaum環と等式$I^2 = QI$，明治大学理工学部研究報告，27-83(2002), 13-17
[86] S. Goto, F. Hayasaka and S. Iai, The $\roman{a}$-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings, Proc. Amer. Math. Soc., 131(2003), 87"94
[87] S. Goto and K. Nishida, Hilbert coefficients and Buchsbaumness of associated graded rings, J. Pure and Appl. Alg., 181(2003), 61-74
[88] S. Goto and Y. Shimoda, Parametric decomposition of powers of ideals versus regularity of sequences, Proc. Amer. Math. Soc., 132-4(2003), 929-933
[89] S. Goto, F. Hayasaka, and S. Kasuga, Towards a theory of Gorenstein m-primary integrally closed ideals, J. Herzog and V. Vuletescu (eds.), Commutative Algebra, Singularities and Computer Algebra, 159-177; The Proceedings of NATO Advanced Research Workshop : Sinaia (Romania), September 17-22, 2002
[90] S. Goto and H. Sakurai, The equality $I^2 = QI$ in Buchsbaum rings, Rendiconti del Seminario Matematico dell'Universit di Padova, 110(2003), 25-56
[91] S. Goto and H. Sakurai, The reduction exponent of socle ideals associated to parameter ideals in a Buchsbaum local ring of multiplicity two, J. Math. Soc. Japan, 56(2004), 1157-1168
[92] S. Goto and Y. Shimoda, On the parametric decomposition of powers of parameter ideals in a Noetherian local ring, Tokyo J. Math., 27-1(2004), 125-135
[93] 後藤四郎・早坂太，安定局所環の構造，明治大学理工学部研究報告，30(2003), 1-6
[94] 松岡直之・後藤四郎，巴系イデアルの冪の整閉性と局所環の正則性について，明治大学理工学部研究報告，30(2003), 7-11
[95] 松岡直之・後藤四郎，２次元単項式イデアルのRatliff-Rush閉包とRees代数のBuchsbaum性について，明治大学理工学部研究報告，32(2005), 37-43
[96] S. Goto and H. Sakurai, When does the equality $I^2 = QI$ hold true in Buchsbaum rings ?, the Special Volume on 'Commutative Algebra with a focus on geometric and homological aspects', Proceedings of Sevilla, June 18-21, 2003 and Lisbon, June 23-27, 2003 to appear in Marcel Dekker's Lecture Notes in Pure and Applied Mathematics Series, 244(2005), 115-139
[97] S. Goto and S. Iai, Gorenstein graded rings associated ideals , J. Algebra, 294(2005), 373-407
[98] S. Goto and S. Iai, Gorenstein graded rings associated to ideals, CRM Preprint No. 540, May, 2003
[99] S. Goto, F. Hayasaka, K. Kurano and Y. Nakamura, Rees algebras of the second syzygy module of the residue field of a regular local ring, Contemporary Mathematics (to appear)
[100] S. Goto, W. Heinzer, and Mee-Kyoung Kim, The leading ideal of a complete intersection of height two, J. Algebra (to appear)
[101] S. Goto and K. Yamagishi, The theory of unconditioned strong d-sequences and modules of finite local cohomology, Preprint

II. 後藤四郎 研究業績（講演）1999年以降
[1] Good ideals in Gorenstein local rings, International Conference on Commutative Algebra, KIAS （韓国), 1999年5月18日-21日
[2] Good ideals in Gorenstein local rings, Commutative Algebra and Algebraic Geometry, Oberwolfach (ドイツ), 1999年8月9日-13日
[3] Good ideals in Gorenstein local rings, 第21回可換環論シンポジウム，東京 (日本), 1999年11月23日- 26日
[4] Good ideals in Gorenstein local rings and related topics, Conference on Commutative Algebra, Algebraic Geometry, and Singularity Theory, A tribute to Manfred Herrmann, Max Plank Institut fuer Mathematik, Bonn (ドイツ), 2000年6月2日-3日
[5] Complete intersection in overrings of a certain one-dimensional Gorenstein graded local ring, International Conference on Commutative Algebra and Algebraic Geometry, CIRM, Luminy (フランス), 2000年6月5日-9日
[6] The $\roman{a}$-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings, Conference on Commutative Algebra 2001, 横浜（日本），2001年8月20日-25日
[7] When I^2 = QI?, 第23回可換環論シンポジウム，倉敷 (日本), 2001年11月19日-22日
[8] 早坂太○・後藤四郎：射影次元有限な整閉イデアルについて, 日本数学会年会（明治大学），2002年3月30日
[9] 居相真一郎○・後藤四郎：Gorenstein graded rings associated to ideals, 日本数学会年会（明治大学），2002年3月30日
[10] Finite homological dimension and primes associated to integrally closed ideals, Current trends in Commutative Algebra, Levico (Trent, Italy), 2002年6月17日-21日
[11] Towards a theory of Gorenstein $\frak{m}$-primary integrally closed ideals, NATO Advanced Research Workshop : Commutative Algebra, Singularities and Computer Algebra, Sinaia (Romania), September 17-22, 2002
[12] 後藤四郎・下田保博○：Parametric decomposition of powers of ideals，第24回可換環論シンポジウム，大阪 (日本), 2002年11月5日-8日
[13] The equality I^2 = QI in Buchsbaum local rings, Commutative algebra and its interaction with algebraic geometry, CIRM in Luminy (France), June 2-6, 2003
[14] The equality I^2 = QI in Buchsbaum rings, Lisbon Conference on Commutative Algebra, Lisbon (Portugal), June 23-27, 2003
[15] 後藤四郎：Buchsbaum 局所環と等式I^2=QI，第48回代数学シンポジウム，名古屋大学（名古屋），2003年8月4日-7日
[16] 後藤四郎：Stable local rings，第25回可換環論シンポジウム，東京, 2003年11月10日-13日
[17] 後藤四郎, On the associated graded rings of certain m-primary ideals in a generalized Cohen-Macaulay local ring，Commutative Algebra and Algebraic Geometry in honor of Professor Masayoshi Miyanishi on the occasion of his retirement, Toyonaka Campus, Osaka University (Osaka, Japan), March 1-5, 2004
[18] 後藤四郎, The equality $I^2 = QI$ in FLC local rings, The International Workshop on Commutative Algebra and its Interaction to  Algebraic Geometry and Combinatorics, The Abdus Salam International Center for Theoretical Physics (Trieste, Italy),  May 24-June 11, 2004
[19] 後藤四郎, Noether安定局所環の構造，Conference on Commutative Algebra and Algebraic Geometry for the memory of Tetsushi Ogoma, Kochi University (Kochi, Japan), August 4-6, 2004
[20] 後藤四郎, Stable local rings, The BIRS workshop, Commutative Algebra : Homological and Birational Theory Dates, Banff International Research Station (Banff, Canada), September 11 - 16, 2004
[21] 後藤四郎・櫻井秀人○，Buchsbaumness of Rees algebras and associated graded rings with respect to socle ideals of subsystem of parameters in Buchsbaum local rings, 第 26 回可換環論シンポジウム，倉敷アイビースクエア ，2004 年 11 月 27 日
[22] 後藤四郎，The leading form ideal of a complete intersection of height 2，第27回可換環論シンポジウム，富山, 2005年11月14日-17日
[23] 後藤四郎・松岡直之○，The Rees algebras of ideals in two dimensional regular local rings，第27回可換環論シンポジウム，富山, 2005年11月14日-17日
[24] 後藤四郎・吉田健一○，Buchsbaum rings with minimal multiplicity，第27回可換環論シンポジウム，富山, 2005年11月14日-17日

III.  後藤四郎 研究業績（シンポジウム報告集論文）1999年以降
[1] Good ideals in Gorenstein local rings, 第21回可換環論シンポジウム報告集 (1999), 1-8
[2] 後藤四郎・居相真一郎，Gorenstein associated graded rings of analytic deviation two ideals,  第22回可換環論シンポジウム報告集 (2000), 33-45
[3] いつ等式I^2=QIが成り立つか？，第23回可換環論シンポジウム報告集 (2001), 126-131
[4] 後藤四郎・下田保博：Parametric decomposition of powers of ideals，第24回可換環論シンポジウム報告集 (2002), 142-147
[5] 後藤四郎，Buchsbaum 局所環と等式I^2=QI，第48回代数学シンポジウム報告 (2003), 156-165
[6] 後藤四郎，Stable local rings，第25回可換環論シンポジウム報告集 (2003), 1-10
[7] 後藤四郎，Noether安定局所環の構造，Conference on Commutative Algebra and Algebraic Geometry for the memory of Tetsushi Ogoma, Kochi University (Kochi, Japan), August 4-6,
2004，報告集(2004)，82-93
[8] 後藤四郎・櫻井秀人，Buchsbaumness of Rees algebras and associated graded rings with respect to socle ideals of subsystem
of parameters in Buchsbaum local rings, 第26回可換環論シンポジウム報告集（2004), 132-140
[9] 後藤四郎，The leading form ideal of a complete intersection of height 2，第27回可換環論シンポジウム報告集 (2005)，
[10] 後藤四郎・松岡直之，The Rees algebras of ideals in two dimensional regular
local rings，第27回可換環論シンポジウム報告集 (2005)，
[11] 後藤四郎・吉田健一，Buchsbaum rings with minimal multiplicity，第27回可換環論シンポジウム報告集 (2005)，