2012 Fiscal Year Final Research Report
Commutative algebra - towards a better understanding of non-Cohen-Macaulay rings
| Project/Area Number |
22540054
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Meiji University |
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Principal Investigator |
GOTO Shiro 明治大学, 理工学部, 教授 (50060091)
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| Co-Investigator(Kenkyū-buntansha) |
OZEKI Kazuho 山口大学, 大学院・理学研究科, 専任講師 (70445849)
IAI Shinichiro 北海道教育大学, 教育学部, 准教授 (50333125)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 環論(含リー環) |
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| Research Abstract |
The final goal of this research is to answer the naive but important question of what non-Cohen-Macaulay rings are. The present targets are the following. (1) The study of quasi-socle ideals Q : mq, where m is the maximal ideal in a given Noetherian local ring and Q a parameter ideal in it. (2) The analysis of the graded rings associated to I = Q : mq. (3) The study of Gorenstein property in the Rees algebras of powers of parameter ideals. The achievements are summarized into 15 papers.
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Research Products
(27 results)
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[Presentation] Ulrich ideals and modules, I2012
Author(s)
後藤四郎
Organizer
The 12-th ALGA Meeting dedicated to Steven Kleiman and Aron Simis on the occasion of their 70-th birthdays
Place of Presentation
IMPA, Rio de Janeiro, Brazil
Year and Date
20120813-17
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[Presentation] Ulrich ideals and modules2012
Author(s)
後藤四郎
Organizer
Commutative Algebra Program of MSRI, Fall 2012 ～ March 2013, the Seminar organized by C. Huneke, C. Polini, and B. Ulrich
Place of Presentation
MSRI, Berkeley, USA.
Year and Date
2012-09-17
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[Presentation] Almost Gorenstein rings2011
Author(s)
後藤四郎
Organizer
Midwest Commutative Algebra and Geometry Conference at PURDUE
Place of Presentation
Purdue University (West Lafayette, USA)
Year and Date
20110522-26
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