Structure of almost Gorenstein rings and Ulrich modules

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400051
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Meiji University
• Principal Investigator: Goto Shiro 明治大学, 理工学部, 教授 (50060091)
• Co-Investigator(Kenkyū-buntansha): IAI Shin-ichiro 北海道教育大学, 教育学部, 准教授 (50333125)
• Co-Investigator(Renkei-kenkyūsha): TRAN Thi Phuong 明治大学, 研究知財戦略機構, ポストドクター (00649824)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: Cohen-Macaulay ring / Canonical module / Almost Gorenstein ring / Ulrich module / Gorenstein ring

Outline of Final Research Achievements

The notion of almost Gorenstein local ring given by V. Barucci and R. Froeberg for one-dimensional analytically unramified Noetherian local rings is generalized for arbitrary Noetherian local rings and a basic theory is developed. The higher dimensional definition is safely introduced also for Noetherian local/graded rings. The theory of almost Gorenstein Rees algebras associated to ideals is well developed and there are obtained satisfactory results in the case where the base rings are regular local rings or the case where the ideals are generated by subsystems of parameters in Cohen-Macaulay local rings.

Free Research Field

代数学（可換環論）