Organization
Undergraduate School School of Science and Technology Professor
Title
Professor
Other name(s)
MATSUOKA Naoyuki
External link
Research Areas
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Natural sciences / Algebra
Education
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明治大学大学院 理工学研究科 基礎理工学専攻数学系博士後期課程
2005.4 - 2008.3
Country/Region： Japan
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Meiji University
2003.4 - 2005.3
Country/Region： Japan
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Meiji University School of Science and Technology Department of Mathematics
1999.4 - 2003.3
Country/Region： Japan
Research History
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明治大学理工学部数学科 専任教授
2024.4
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明治大学理工学部数学科 専任准教授
2018.10 - 2024.3
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明治大学理工学部数学科 専任講師
2014.4 - 2018.9
Country/Region：Japan
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株式会社オクタル・ジャポン
2012.4 - 2014.3
Country/Region：Japan
Professional Memberships
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日本数学会
Papers
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An upper bound for the Frobenius number and stretched numerical semigroups Reviewed
Kazufumi Eto, Naoyuki Matsuoka, Takahiro Numata, Kei-ichi Watanabe
Communications in Algebra 2025.11
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Rings with <i>q</i>-torsionfree canonical modules Reviewed
Naoki Endo, Laura Ghezzi, Shiro Goto, Jooyoun Hong, Shin-ichiro Iai, Toshinori Kobayashi, Naoyuki Matsuoka, Ryo Takahashi
Commutative Algebra - The Mathematical Legacy of Wolmer V. Vasconcelos 405 - 426 2025.9
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Nearly Gorenstein local rings defined by maximal minors of a $$2 \times n$$ matrix Reviewed
Shinya Kumashiro, Naoyuki Matsuoka, Taiga Nakashima
Semigroup Forum 2025.2
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Almost Gorenstein simplicial semigroup rings Reviewed
Kazufumi Eto, Naoyuki Matsuoka, Takahiro Numata, Kei-ichi Watanabe
Journal of Pure and Applied Algebra 2025.1
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Ulrich ideals in the ring k[[t5,t11]] Reviewed
Naoki Endo, Shiro Goto, Shin-ichiro Iai, Naoyuki Matsuoka
International Journal of Algebra and Computation 2024.5
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Remarks on almost Gorenstein rings Reviewed
Naoki Endo, Naoyuki Matsuoka
Communications in Algebra 52 ( 7 ) 2884 - 2891 2024
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ON THE WEAKLY ARF (S2)-IFICATIONS OF NOETHERIAN RINGS Reviewed
Naoki Endo, Shiro Goto, Shin-ichiro Iai, Naoyuki Matsuoka
Journal of Commutative Algebra 15 ( 3 ) 2023.9
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ON THE UBIQUITY OF ARF RINGS Reviewed
Ela Celikbas, Olgur Celikbas, Cătălin Ciupercă, Naoki Endo, Shiro Goto, Ryotaro Isobe, Naoyuki Matsuoka
Journal of Commutative Algebra 15 ( 2 ) 2023.6
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When are the rings <i>I:I</i> Gorenstein? Reviewed
Naoki Endo, Shiro Goto, Shin-ichiro Iai, Naoyuki Matsuoka
Communications in Algebra 51 ( 4 ) 1721 - 1734 2022.11
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EFFICIENT GENERATION OF IDEALS IN CORE SUBALGEBRAS OF THE POLYNOMIAL RING k[t] OVER A FIELD k Reviewed
Naoki Endo, Shiro Goto, Naoyuki Matsuoka, Yuki Yamamoto
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 148 ( 8 ) 3283 - 3292 2020.8
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Numerical Semigroup Rings of Maximal Embedding Dimension with Determinantal Defining Ideals Reviewed
Do Van Kien, Naoyuki Matsuoka
Numerical Semigroups 185 - 196 2020.5
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On the almost Gorenstein property in Rees algebras of contracted ideals Reviewed
Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi, Ken-ichi Yoshida
Kyoto Math. J. 59 ( 4 ) 769 - 785 2019.12
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Sally modules of canonical ideals in dimension one and 2-AGL rings Reviewed
Tran Do Minh Chau, Shiro Goto, Shinya Kumashiro, Naoyuki Matsuoka
Journal of Algebra 521 299 - 330 2019.3
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Pseudo-Frobenius numbers versus defining ideals in numerical semigroup rings Reviewed
Shiro Goto, Do Van Kien, Naoyuki Matsuoka, Hoang Le Truong
Journal of Algebra 508 1 - 15 2018.8
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Almost Gorenstein Rees Algebras of p(g)-Ideals, Good Ideals, and Powers of the Maximal Ideals Reviewed
Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi, Ken-Ichi Yoshida
MICHIGAN MATHEMATICAL JOURNAL 67 ( 1 ) 159 - 174 2018
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The almost Gorenstein Rees algebras over two-dimensional regular local rings Reviewed
Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi, Ken-ichi Yoshida
JOURNAL OF PURE AND APPLIED ALGEBRA 220 ( 10 ) 3425 - 3436 2016.10
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Uniformly Cohen-Macaulay simplicial complexes and almost Gorenstein* simplicial complexes Reviewed
Naoyuki Matsuoka, Satoshi Murai
JOURNAL OF ALGEBRA 455 14 - 31 2016.6
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The almost Gorenstein Rees algebras of parameters Reviewed
Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi, Ken-ichi Yoshida
JOURNAL OF ALGEBRA 452 263 - 278 2016.4
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Almost Gorenstein rings Reviewed
Shiro Goto, Naoyuki Matsuoka, Tran Thi Phuong
JOURNAL OF ALGEBRA 379 355 - 381 2013.4
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Kazuhiko Kurano, Naoyuki Matsuoka
JOURNAL OF ALGEBRA 322 ( 9 ) 3268 - 3290 2009.11
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Quasi-Socle ideals in local rings with Gorenstein tangent cones Reviewed
Shiro Goto, Satoru Kimura, Naoyuki Matsuoka
Journal of Commutative Algebra 1 ( 4 ) 603 - 620 2009
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Quasi-socle ideals in Gorenstein numerical semigroup rings Reviewed
Shiro Goto, Satoru Kimura, Naoyuki Matsuoka
JOURNAL OF ALGEBRA 320 ( 1 ) 276 - 293 2008.7
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Quasi-socle ideals in a Gorenstein local ring Reviewed
Shiro Goto, Ryo Takahashi, Naoyuki Matsuoka
JOURNAL OF PURE AND APPLIED ALGEBRA 212 ( 5 ) 969 - 980 2008.5
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On m-full powers of parameter ideals Reviewed
Naoyuki Matsuoka
Tokyo Journal of Mathematics 29 ( 2 ) 405 - 411 2006
MISC
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数値半群環の stretched 性に関するテストエレメントについて Reviewed
生熊 克健, 松岡 直之
明治大学理工学部研究報告 57 ( 57 ) 1 - 9 2023.3
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The structure of quasi-parameter ideals and their associated graded rings
松岡 直之
1 - 70 2008
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Quasi-socle ideals in gorenstein numerical semi-group rings
Research reports,School of Science and Technology,Meiji University ( 36 ) 1 - 8 2007
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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
松岡, 直之, 後藤, 四郎
明治大学理工学部研究報告 32 37 - 43 2005.3
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松岡 直之, 後藤 四郎
明治大学理工学部研究報告 30 ( 30 ) 7 - 11 2003
Presentations
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Stretched semigroup rings and 2-minor generation in defining ideals
Kazufumi Eto, Naoyuki Matsuoka, Takahiro Numata, Kei-ichi Watanabe
2025.11
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3変数多項式環の単項式イデアルの正規性について Invited
松岡直之
Commutative Algebra Days in Kirishima 2025.10
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An upper bound for the Frobenius number and stretched numerical semigroups
Kazufumi Eto, Naoyuki Matsuoka, Takahiro Numata, Kei-ichi Watanabe
2024.11
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Numerical semigroup rings - A foundation of combinatorial perspective on commutative algebra
Naoyuki Matsuoka
Interactions of Commutative Algebra, Representation Theory, and Combinatorics in Bangkok 2024.10
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Nearly Gorenstein local rings defined by maximal minors of a $2 \times n$ matrix
Naoyuki Matsuoka
2024.7
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1次元解析を基盤とした局所環論 Invited
松岡 直之
第68回代数学シンポジウム 2023.8
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Numerical semigroup rings with determinantal defining ideals Invited
Naoyuki Matsuoka
One day workshop on Commutative Algebra 2023.2
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Defining ideals of affine monomial curves in A^4 and associated projective monomial curves in P^4
衛藤 和文, 松岡 直之, 沼田 崇宏, 渡辺 敬一
第43回可換環論シンポジウム 2022.11
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Ulrich ideals in numerical semigroup rings Invited
松岡 直之
東京可換環論セミナー 2021.10
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Efficient generation of ideals in core subalgebras of the polynomial ring k[t] over a field k
Naoyuki Matsuoka
The 8th China–Japan–Korea International Symposium on Ring Theory 2019.8
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The GGL property of numerical semigroup rings obtained by gluing Invited
Naoyuki Matsuoka
The 10th Japan-Vietnam Joint Seminar on Commutative Algebra 2018.9
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The generalized Gorenstein property and numercal semigroup rings obtained by gluing Invited
Naoyuki Matsuoka
INdAM meeting : international meeting on numerical semigroups 2018.9
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Pseudo-Frobenius numbers versus defining ideals in numerical semigroup rings
松岡直之
第39回可換環論シンポジウム 2017.11
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Pseudo-Frobenius numbers versus defining ideals in numerical semigroup rings Invited
Naoyuki Matsuoka
International Conference on Commutative Algebra and its Interactions to Combinatorics, Discrete Geometry and Singularity Theory 2017.9
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Pseudo-Frobenius numbers and the generation of the defining ideal
松岡直之
第28可換環論セミナー 2017.2
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The minimal free resolution of a numerical semigroup ring with arithmetic pseudo-Frobenius numbers of type 3 Invited
Naoyuki Matsuoka
Japan-Vietnam Workshop on Commutative Algebra, 2016 -by and for young mathematicians- 2016.9
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The almost Gorenstein Rees algebras of contracted ideals
後藤四郎, 松岡直之, 谷口直樹, 吉田健一
2016年 日本数学会年会 2016.3
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On the almost Gorenstein property in Rees algebras of contracted ideals Invited
Naoyuki Matsuoka
The 8th Japan-Vietnam Joint Seminar on Commutative Algebra 2016.3
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Minimal free resolutions of certain almost Gorenstein numerical semigroup rings Invited
Naoyuki Matsuoka
2016.1
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The almost Gorenstein Rees algebras of socle ideals
後藤四郎, 松岡直之, 谷口直樹, 吉田健一
2015年 日本数学会秋季年会 2015.9
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The almost Gorenstenness of Rees algebras of contracted ideals in 2-dimensional regular local rings Invited
2015.9
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2次元正規特異点のpg-idealのRees代数のAlmost Gorenstein性
後藤四郎, 松岡直之, 谷口直樹, 吉田健一
2015年 日本数学会秋季年会 2015.9
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Almost Gorenstein rings Invited
Naoyuki Matsuoka
INdAM meeting: International meeting on numerical semigroups 2014.9
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Basic properties of one-dimensional almost Gorenstein rings Invited
松岡直之
第8回大和郡山セミナー 2012.1
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Applications of one-dimensional almost Gorenstein rings Invited
松岡直之
第8回大和郡山セミナー 2012.1
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Almost Gorenstein rings — One dimensional case Invited
Naoyuki Matsuoka
The 7th Japan-Vietnam Joint Seminar on Commutative Algebra 2011.12
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Almost Gorenstein rings
後藤四郎, 松岡直之, Tran Thi Phuong
第33回可換環論シンポジウム 2011.11
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Almost Gorenstein rings Invited
松岡直之
第6回大和郡山セミナー 2011.8
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2変数単項式イデアルのRatliff-Rush閉包について Invited
松岡直之
第2回大和郡山セミナー 2010.10
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Divisor class groups of algebras of minors
松岡直之
第7回可換環論サマースクール 2010.8
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ASL structure and determinantal ideals Invited
松岡直之
第7回可換環論サマースクール 2010.8
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Quasi-socle ideals in Gorenstein numerical semigroup rings
後藤四郎, 木村了, 松岡直之
2008年 日本数学会春季年会 2008.3
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Quasi-socle ideals in local rings with Gorenstein tangent cones
後藤四郎, 木村了, 松岡直之
2008年 日本数学会春季年会 2008.3
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Quasi-socle ideals in a Gorenstein local ring Invited
he Third Japan-Vietnam Joint Seminar on Commutative Algebra 2007.12
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Quasi-socle ideals in local rings with Gorenstein tangent cones
後藤四郎, 木村了, 松岡直之, Tran Thi Phuong
第29回可換環論シンポジウム 2007.11
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Quasi-socle ideals in a Gorenstein local ring
後藤四郎, 松岡直之, 高橋亮
2007年 日本数学会秋季年会 2007.9
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Quasi-socle ideals in a Gorenstein local ring
松岡直之
第19回可換環論セミナー 2007.1
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Macaulay2によるfree resolutionの計算 Invited
松岡直之
第3回可換環論サマースクール 2006.9
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The 2nd Japan-Vietnam Joint Seminar on Commutative Algebra Invited
Naoyuki Matsuoka
The 2nd Japan-Vietnam Joint Seminar on Commutative Algebra 2006.3
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The Rees algebras of ideals in two dimensional regular local rings
後藤四郎, 松岡直之
2006年 日本数学会春季年会 2006.3
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The Rees algebras of ideals in two dimensional regular local rings, II
松岡直之
第18回可換環論セミナー 2006.1
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The Rees algebras of ideals in two dimensional regular local ring
後藤四郎, 松岡直之
第27回可換環論シンポジウム 2005.11
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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
後藤四郎, 松岡直之
2005年 日本数学会秋季年会 2005.9
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Ratliff-Rush closures of certain 2-dimensional monomial ideals and Buchsbaumness of its Rees algebras Invited
Naoyuki Matsuoka
2005.5
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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
松岡直之
第10回代数学若手研究集会 2005.3
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単項式イデアルのRatliff–Rush閉包について
松岡直之
第17回可換環論セミナー 2005.1
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単項式イデアルのRatliff–Rush閉包について
松岡直之
第26回可換環論シンポジウム 2004.11
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巴系イデアルの冪の整閉性と局所環の正則性について
松岡直之
第16回可換環論セミナー 2004.1
Research Projects
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A New Approach to the Classification of Local Rings via Deviations from Gorensteinness
Grant number：25K06941 2025.4 - 2028.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Grant amount：\4680000 （ Direct Cost: \3600000 、 Indirect Cost：\1080000 ）
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Weak Arf closures of rings versus their strict closures
Grant number：21K03211 2021.4 - 2023.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Grant amount：\4160000 （ Direct Cost: \3200000 、 Indirect Cost：\960000 ）
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概Gorenstein環論の形成と発展
Grant number：18K03227 2018.4 - 2021.3
日本学術振興会 科学研究費助成事業 基盤研究(C) 基盤研究(C)
松岡 直之, 後藤 四郎, チャン ティフン
Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）
本研究の目的は、Gorenstein性と非Gorenstien性の間に横たわる溝を埋めるような局所環のクラスを探究することで非Gorenstein環の階層化を実現せしめ、非Gorenstein環解析に新たな展開をもたらすことにある。
本年度までに実施した研究課題は大きく分けて(1) Rees代数のalmost Gorenstein性解析、(2) 2-almost Gorenstein環の定義と基礎理論構築、(3) 数値半群環の極小自由分解の構造解析の3種類である。
(1)では、研究分担者である後藤四郎氏と、協力者である谷口直樹氏・吉田健一氏との間で継続して行ってきた共同研究を発展させ、いかなるイデアルのRees代数がalmost Gorensteinとなり得るかを追求した。その過程において、almost Gorenstein環はGorenstein環と比べ枠組みを広げることには成功しているものの、未だに希少であると判明した。これが (2)の研究動機であり、2-almost Gorenstein環の定義に至った。与えられた次数環の情報の多くは、その極小自由分解が含んでいると考えられる。ベッチ数など、極小自由分解に付随する不変量の解析は盛んに行われているが、その構造を写像の形まで含めて確定させる研究は多くなく、数値半群環に関しても知られていることは少ない。研究(3)は、数値半群の擬フロベニウス数と半群環の定義イデアルとの関係性に着目し、ある種の数値半群環の極小自由分解の構造を完全に特定したものである。
本研究内容は論文にまとめ国際的な数学専門誌へ投稿している。また、国際研究集会においても講演した。
第40回可換環論シンポジウムを、本研究経費でその開催経費の一部を負担して開催した（下元数馬氏、吉田健一氏（共に日本大学）と共同開催）。 -
Study of almost Gorenstein rings
Grant number：16K05112 2016.4 - 2021.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Goto Shiro
Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）
The research aims at the classification of non-Gorenstein Cohen-Macaulay rings in terms of the distance from Gorenstein rings. The notion of almost Gorenstein ring was given in 2015 by [1] as a higher-dimensional generalization of the notion defined in 1997 by [2] (resp. in 2013 by [3]) for analytically unramified (resp. arbitrary) Cohen-Macaulay local rings of dimension one. The proposed and achieved tasks are the following. (1) Deepening of the theory of almost Gorenstein local/graded rings started by [1]. (2) Analysis of the almost Gorenstein property of Rees algebras of parameter ideals in Cohen-Macaulay local rings, and those of integrally closed/contracted ideals in two-dimensional regular local rings. (3) Permeation of the notion of almost Gorenstein ring into other branches of algebra, for examples, algebraic geometry, combinatorics, invariant theory.
[1] J. Pure and Appl. Algebra, 219 (2015), 2666-2712. [2] J. Algebra, 188 (1997), 418-442. [3] J. Algebra, 379 (2013), 355-381. -
Developement of the theory of non-Gorenstein rings and a study of j-multiplicity
Grant number：26400054 2014.4 - 2018.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) Grant-in-Aid for Scientific Research (C)
Tran Thi Phuong, GOTO Shiro
Grant amount：\4680000 （ Direct Cost: \3600000 、 Indirect Cost：\1080000 ）
The purpose of this research is to enrich the theory of one-dimensional almost Gorenstein rings, which was originally studied by Barucci-Froeberg and Goto-Matsuoka-Phuong, and to develop the theory for higher dimension. Among them, we studied the almost Gorenstein property for Rees algebras, determinantal rings, and Arf rings. In parallel, we analyzed the sequentially Cohen-Macaulay property for the Rees algebras in order to make progress the theory of non-Cohen-Macaulay rings and modules.
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