Journal of Commutative Algebra

Systems of parameters and the Cohen-Macaulay property

Katharine Shultis

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Let $R$ be a commutative, Noetherian, local ring and $M$ a finitely generated $R$-module. Consider the module of homomorphisms $Hom _R(R/\mathfrak{a} ,M/\mathfrak{b} M)$ where $\mathfrak{b} \subseteq \mathfrak{a} $ are parameter ideals of $M$. When $M=R$ and $R$ is Cohen-Macaulay, Rees showed that this module of homomorphisms is isomorphic to $R/\mathfrak{a} $, and in particular, a free module over $R/\mathfrak{a} $ of rank one. In this work, we study the structure of such modules of homomorphisms for a not necessarily Cohen-Macaulay $R$-module $M$.

Article information

J. Commut. Algebra, Volume 10, Number 1 (2018), 139-151.

First available in Project Euclid: 18 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13C05: Structure, classification theorems 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Cohen-Macaulay property system of parameters


Shultis, Katharine. Systems of parameters and the Cohen-Macaulay property. J. Commut. Algebra 10 (2018), no. 1, 139--151. doi:10.1216/JCA-2018-10-1-139.

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