A note on Chern coefficients and Cohen-Macaulay rings

TL;DR

This paper explores the connection between Chern coefficients and the index of reducibility in primary ideals, providing characterizations of Cohen-Macaulay rings based on these invariants in Noetherian local rings.

Contribution

It offers new characterizations of Cohen-Macaulay rings using Chern coefficients, irreducible multiplicity, and the type of the ring, linking algebraic invariants.

Findings

Characterization of Cohen-Macaulay rings via Chern coefficients

Relationship established between index of reducibility and Chern coefficients

Criteria involving irreducible multiplicity and type for Cohen-Macaulayness

Abstract

In this paper, we investigate the relationship between the index of reducibility and Chern coefficients for primary ideals. As an application, we give characterizations of a Cohen-Macaulay ring in terms of its type, irreducible multiplicity, and Chern coefficients with respect to certain parameter ideals in Noetherian local rings.