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