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Mathematics > Commutative Algebra

arXiv:0709.1537 (math)
[Submitted on 11 Sep 2007 (v1), last revised 13 Sep 2007 (this version, v2)]

Title:Asymptotic Behaviour of Parameter Ideals in Generalized Cohen-Macaulay Modules

Authors:Nguyen Tu Cuong, Hoang Le Truong
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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) $I^2=\q I$, where $I=\q:_R\m$.
Comments: 12 pages
Subjects: Commutative Algebra (math.AC)
MSC classes: 13H45; 13H10
Cite as: arXiv:0709.1537 [math.AC]
  (or arXiv:0709.1537v2 [math.AC] for this version)
  https://doi.org/10.48550/arXiv.0709.1537

Submission history

From: Nguyen Tu Cuong [view email]
[v1] Tue, 11 Sep 2007 07:52:38 UTC (9 KB)
[v2] Thu, 13 Sep 2007 04:16:15 UTC (9 KB)
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