On the index of reducibility of parameter ideals: The stable and limit values

2019/03/04 by Nguyen Tu Cuong, Cuong, Nguyen Tu, Phạm Hùng Quý +1
Mathematics · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1903.01315

Abstract

Let (R, \frak 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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