Asymptotic Behaviour of Parameter Ideals in Generalized Cohen-Macaulay Modules

Details Asymptotic Behaviour of Parameter Ideals in Generalized Cohen-Macaulay Modules Asymptotic Behaviour of Parameter Ideals in Generalized Cohen-Macaulay Modules

2007-09-11

arxiv.org/abs/0709.1537v2

Mathematics

Commutative Algebra

12 pages

Scientific paper

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 $I=\q:_R\m$.

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