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On the Index of Reducibility of Parameter Ideals: the Stable and Limit Values

Nguyen Tu Cuong , $icon-email$ Pham Hung Quy

Abstract

Let $(R, m)$ be a Noetherian local ring and $M$ a finitely generated $R$ -module of dimension $d$ . A famous result of Northcott says that if $M$ is Cohen-Macaulay, then the index of reducibility of parameter ideals on $M$ is an invariant of the module. The aim of this paper is to extend Northcott’s theorem for any finitely generated $R$ -module. We call this invariant the stable value of the indices of reducibility of parameter ideals of $M$ . We also introduce the limit value of the indices of reducibility of parameter ideals of $M$ .

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On the Index of Reducibility of Parameter Ideals: the Stable and Limit Values

Abstract