Journal of Commutative Algebra

Systems of parameters and the Cohen-Macaulay property

Katharine Shultis

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Abstract

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

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

Dates
First available in Project Euclid: 18 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.jca/1526608938

Digital Object Identifier
doi:10.1216/JCA-2018-10-1-139

Mathematical Reviews number (MathSciNet)
MR3804850

Zentralblatt MATH identifier
06875417

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

Keywords
Cohen-Macaulay property system of parameters

Citation

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. https://projecteuclid.org/euclid.jca/1526608938


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References

  • Kamal Bahmanpour and Reza Naghipour, A new characterization of Cohen-Macaulay rings, J. Alg. Appl. 13 (2014), 1450064, available online at doi.10.1142/S0219498814500649.
  • Bruns Winfried and Jürgen Herzog, Cohen-Macaulay rings, Cambr. Stud. Adv. Math. 39 (1993).
  • D.G. Northcott, Lessons on rings, modules and multiplicities, Cambridge University Press, London, 1968.
  • D. Rees, A theorem of homological algebra, Proc. Cambridge Philos. Soc. 52 (1956), 605–610.