IAI Shin-ichiro 居相真一郎

… Alternative Names

居相真一郎イアイシンイチロウ

Less

Researcher Number	50333125
Other IDs
Affiliation (Current)	2025: 北海道教育大学, 教育学部, 准教授
Affiliation (based on the past Project Information) *help	2007 – 2021: Hokkaido University of Education, Faculty of Education, Associate Professor 2003 – 2006: Hokkaido University of Education, School of Education, Associate Prof., 教育学部, 助教授 2004 – 2005: 北海道教育大学, 教育学部札幌校, 助教授 2002: 北海道教育大学, 教育学部・札幌校, 講師
Review Section/Research Field	Principal Investigator Algebra Except Principal Investigator Algebra / Algebra / Basic Section 11010:Algebra-related
Keywords	Principal Investigator 正準加群 / Gorenstein環 / Rees代数 / generalized Cohen-Macaulay環 / a standard svstem of parameters / Buchsbaum局所環 / 拡大Rees代数 / blow-up代数 / a standard system of parameters / FLC環 / Cohen-Macaulay環 / 随伴次数環 … More Except Principal Investigator … More Cohen-Macaulay環 / 可換環論 / 有限群の表現論 / ブロック多元環 / Gorenstein ring / Cohen-Macaulay ring / Almost Gorenstein ring / Ulrich module / Arf環 / Broue's Conjecture / Splendid Tilting Complexes / Block Algebras / Representations of Finite Groups / ブルエ予想 / 傾斜複体 / Rees代数 / Gorenstein環 / index of reducibility / 整閉イデアル / almost Gorenstein ring / 代数学 / canonical module / Buchsbaum環 / 重複度 / Ulrich ideal / 環のstrict closure / weakly Arf closure / 弱 Arf 環 / Arf 環に関するZariski予想 / Arf 環 / Cohen-Macaulay 環 / 数値半群環 / 弱Arf closure / strict closure / 弱Arf環 / Arf環に関するZariski予想 / commutative algebra / 数学 / 2-almost Gorenstein ring / Contracted ideal / Sally module / 2-AGL ring / Generalized Gorenstein環 / Almost Gorenstein環 / Commutative algebra / contracted ideal / integrally closed ideal / Rees algebra / Cohomology / Complex of Modules / Glauberman Correspondence / Derived Equivalence / Block Algebra / Representation of Finite Group / 加群の複体とコホモロジー / コホモロジー / 加群の複体 / グラウバウマン対応 / 導来同値 / Shintani Descent / 新谷ディセント / filtration / graded ring / local ring / フィルトレーション / 次数付き環 / 局所環 / system of parameters / multiplicity / local cohomology / FLC ring / Buchsbaum ring / Bass数 / Noetheian algebra / 優良イデアル / 正則局所環 / 入射次元 / 射影次元 / homological dimension / a-invariant / FLC局所環 / Cohen-Macaulay局所環 / 局所コホモロジー / Buchsbaum局所環 / Noether局所環 / Ａｌｍｏｓｔ　Ｇｏｒｅｎｓｔｅｉｎ環 / Canonical module / Hilbert係数 / Hilbert函数 / Ulrichイデアル/加群 / almost Gorenstein環 / Hilbert函数とHilbert係数 / generalized Cohen-Macaulay環 / 可換環 / Cohen-Macaualy ring / 環論(含リー環) / ブロックの導来同値 / 群のコホモロジー / 群の表現論 Less

Weak Arf closures of rings versus their strict closures
- Principal Investigator
  
  後藤四郎
- Project Period (FY)
  2021 – 2022
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Meiji University
Study of almost Gorenstein rings
- Principal Investigator
  
  Goto Shiro
- Project Period (FY)
  2016 – 2020
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Meiji University
Structure of almost Gorenstein rings and Ulrich modules
- Principal Investigator
  
  Goto Shiro
- Project Period (FY)
  2013 – 2015
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Meiji University
Commutative algebra - towards a better understanding of non-Cohen-Macaulay rings
- Principal Investigator
  
  GOTO Shiro
- Project Period (FY)
  2010 – 2012
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Meiji University
Studies on fusion systems and cohomology of finite groups
- Principal Investigator
  
  OKUYAMA Tetsuro
- Project Period (FY)
  2008 – 2010
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University of Education
On the Gorensteinness of Rees algebrasPrincipal Investigator
- Principal Investigator
  
  IAI Shin-ichiro
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University of Education
A Study on Glauberman-Watanabe Correspondence and Derived Equivalence of Blocks
- Principal Investigator
  
  OKUYAMA Tetsuro
- Project Period (FY)
  2006 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University of Education
可換環のイデアルのfiltrationに随伴する次数環の代数構造Principal Investigator
- Principal Investigator
  
  居相真一郎
- Project Period (FY)
  2004 – 2006
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University of Education
A Study on Derived Equivalences of Blocks and Shintani Descent in Group Algebras
- Principal Investigator
  
  OKUYAMA Tetsuro
- Project Period (FY)
  2004 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University of Education
Research on the associated graded ring of a general filtration
- Principal Investigator
  
  NISHIDA Koji
- Project Period (FY)
  2003 – 2006
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Chiba University
A Study on Constructions of Splendid Tilting Complexes and Broue's Conjecture
- Principal Investigator
  
  OKUYAMA Tesuro
- Project Period (FY)
  2002 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University of Education
Study of Blowing-up rings
- Principal Investigator
  
  GOTO Shiro
- Project Period (FY)
  2001 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Meiji University

All 2022 2021 2009 2008 2007 2006 2005 Other

All Journal Article Presentation

[Journal Article] On the weakly Arf (S_2)-ifications of Noetherian rings2022
- Author(s)
  N. Endo, S. Goto, S.-i. Iai, N. Matsuoka
- Journal Title
  
  arxiv.org/abs/2204.12132
  
  Volume: -
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-21K03211
[Journal Article] When are the rings $I:I$ Gorenstein?2021
- Author(s)
  N. Endo, S. Goto, S.-i. Iai, N. Matsuoka
- Journal Title
  
  arXiv:2111.13338
  
  Volume: -
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-21K03211
[Journal Article] Ulrich ideals in the ring $k[[t^5, t^{11}]]$2021
- Author(s)
  N. Endo, S. Goto, S.-i. Iai, N. Matsuoka
- Journal Title
  
  arxiv.org/abs/2111.01085
  
  Volume: -
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-21K03211
[Journal Article] Gorenstein graded rings associated to ideals2006
- Author(s)
  S.Goto, S.-i.Iai
- Journal Title
  
  Journal of Algebra (掲載予定)
- Data Source
  KAKENHI-PROJECT-16540001
[Journal Article] Gorenstein graded rings associated to ideals2005
- Author(s)
  S.Goto, S.-i.Iai
- Journal Title
  
  Journal of Algebra 294
  
  Pages: 373-407
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540001
[Journal Article] Gorenstein graded rings associated to ideals2005
- Author(s)
  Shin-Ichiro Iai
- Journal Title
  
  Journal of Algebra Vol.294
  
  Pages: 373-407
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540009
[Journal Article] Gorenstein graded rings associated to ideals2005
- Author(s)
  S.Goto, S.-i.Iai
- Journal Title
  
  J.Algebra 294
  
  Pages: 373-407
- Data Source
  KAKENHI-PROJECT-16740001
[Journal Article] Gorenstein graded rings associated to ideals2005
- Author(s)
  Shin-Ichiro Iai
- Journal Title
  
  Journal of Algebra 294
  
  Pages: 373-407
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540009
[Journal Article] When are the rings $I:I$ Gorenstein?
- Author(s)
  Naoki Endo, Shiro Goto, Shin-ichiro Iai, Naoyuki Matsuoka
- Journal Title
  
  Communications in Algebra
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21K03211
[Journal Article] On the weakly Arf (S_2)-ifications of Noetherian rings
- Author(s)
  Noki Endo, Shiro Goto, Shin-ichiro Iai, Naoyuki Matsuoka
- Journal Title
  
  Journal of Commutative Algebra
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21K03211
[Presentation] Gorenstein Rees algebras over generalized Cohen-Macaulay rings of depth one2009
- Author(s)
  Shin-ichiro Iai
- Organizer
  The 4th Japan-Vietnam Joint Seminar on Commutative Algebra
- Place of Presentation
  川崎
- Year and Date
  2009-02-18
- Data Source
  KAKENHI-PROJECT-19740001
[Presentation] Gorenstein Rees algebras over rings of depth one having finite local cohomology2009
- Author(s)
  居相真一郎
- Organizer
  第31回可換環論シンポジウム
- Place of Presentation
  ホテルアウィーナ大阪
- Year and Date
  2009-11-24
- Data Source
  KAKENHI-PROJECT-20540001
[Presentation] Gorenstein Rees algebras over generalized Cohen-Macaulay rings of depth one2009
- Author(s)
  Shin-ichiro Iai
- Organizer
  The 4^<th> Japan-Vietnam Joint Seminar on Commutative Algebra
- Place of Presentation
  明治大学
- Year and Date
  2009-02-18
- Data Source
  KAKENHI-PROJECT-19740001
[Presentation] Gorenstein Rees algebras over rings of depth one having finite local cohomology2009
- Author(s)
  居相真一郎
- Organizer
  第31回可換環論シンポジウム
- Place of Presentation
  ホテルアウィーナ大阪
- Year and Date
  2009-11-26
- Data Source
  KAKENHI-PROJECT-19740001
[Presentation] Gorenstein Rees algebras over rings of depth one having finite local cohomology2009
- Author(s)
  居相真一郎
- Organizer
  第31回可換環論シンポジウム
- Place of Presentation
  大阪
- Year and Date
  2009-11-26
- Data Source
  KAKENHI-PROJECT-19740001
[Presentation] On Gorenstein Rees algebras2008
- Author(s)
  Shin-ichiro Iai
- Organizer
  International Conference on Commutative Algebra
- Place of Presentation
  横浜
- Year and Date
  2008-03-21
- Data Source
  KAKENHI-PROJECT-19740001
[Presentation] The blowup algebras over rings with finite local cohomology2007
- Author(s)
  居相真一郎
- Organizer
  第29回可換環論シンポジウム
- Place of Presentation
  名古屋
- Year and Date
  2007-11-20
- Data Source
  KAKENHI-PROJECT-19740001
[Presentation] On Gorenstein Rees algebras over rings with finite local cohomology2007
- Author(s)
  Shin-ichiro Iai
- Organizer
  The 3rd Japan-Vietnam Joint Seminar on Commutative Algebra
- Place of Presentation
  ベトナム国
- Year and Date
  2007-12-03
- Data Source
  KAKENHI-PROJECT-19740001
[Presentation] The blowup algebras over rings with Finite local cohomology2007
- Author(s)
  居相真一郎
- Organizer
  第29回可換環論シンポジウム
- Place of Presentation
  名古屋
- Year and Date
  2007-11-20
- Data Source
  KAKENHI-PROJECT-19740001

1. GOTO Shiro (50060091)

# of Collaborated Projects: 5 results

# of Collaborated Products: 5 results
2. OKUYAMA Tetsuro (60128733)

# of Collaborated Projects: 4 results

# of Collaborated Products: 0 results
3. YATSUI Tomoaki (00261371)

# of Collaborated Projects: 4 results

# of Collaborated Products: 0 results
4. KITAYAMA Masashi (80169888)

# of Collaborated Projects: 4 results

# of Collaborated Products: 0 results
5. HASEGAWA Izumi (50002473)

# of Collaborated Projects: 3 results

# of Collaborated Products: 0 results
6. SASAKI Hiroki (60142684)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
7. KOMURO Naoto (30195862)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
8. FUKUI Masaki (20002628)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
9. ABE Osamu (30202659)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
10. 松岡直之 (80440155)

# of Collaborated Projects: 2 results

# of Collaborated Products: 5 results
11. OZEKI Kazuho (70445849)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
12. TRAN Thi Phuong (00649824)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
13. KAMOI Yuji (80308064)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
14. NAKAMURA Yukio (00308066)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
15. KURANO Kazuhiko (90205188)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
16. NISHIDA Koji (60228187)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
17. KOSHITANI Shigeo (30125926)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
18. MATSUDA Shigeki (90272301)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
19. OKUBO Kazuyoshi (80113661)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results

IAI Shin-ichiro 居相 真一郎

居相 真一郎 イアイ シンイチロウ

Research Projects

Research Products

Co-Researchers

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

On the Gorensteinness of Rees algebrasPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

可換環のイデアルのfiltrationに随伴する次数環の代数構造Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] On the weakly Arf (S_2)-ifications of Noetherian rings2022

Author(s)

Journal Title

Data Source

[Journal Article] When are the rings $I:I$ Gorenstein?2021

Author(s)

Journal Title

Data Source

[Journal Article] Ulrich ideals in the ring $k[[t^5, t^{11}]]$2021

Author(s)

Journal Title

Data Source

[Journal Article] Gorenstein graded rings associated to ideals2006

IAI Shin-ichiro 居相真一郎

居相真一郎イアイシンイチロウ