Asymptotic Behaviour of Parameter Ideals in Generalized Cohen-Macaulay Modules

2007/09/11 by Nguyen Tu Cuong, Cuong, Nguyen Tu, Hoang Le Truong +1
Computer Science · Mathematics · #13H10 #13H45 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13H10 #msc:13H45

paper · pdf · doi:10.48550/arxiv.0709.1537

12 pages

openalex publication_date 2007/09/11 · arxiv created 2007/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to give affirmative answers to two open questions as follows. Let (R, \m) be a generalized Cohen-Macaulay Noetherian local ring. Both questions, the first question was raised by M. Rogers \cite R and the second one is due to S. Goto and H. Sakurai \cite GS1, ask whether for every parameter ideal \q contained in a high enough power of the maximal ideal \m the following statements are true: (1) The index of reducibility N_R(\q;R) is independent of the choice of \q; and (2) I²=\q I, where I=\q:_R\m.

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