Eventually index of reducibility on sequentially Cohen-Macaulay modules

TL;DR

This paper characterizes sequentially Cohen-Macaulay modules through the eventual constancy of the index of reducibility for distinguished parameter ideals, and applies these results to characterize Gorenstein and Cohen-Macaulay local rings.

Contribution

It establishes a new criterion for sequentially Cohen-Macaulay modules based on the behavior of the index of reducibility, linking module properties to ideal invariants.

Findings

Sequentially Cohen-Macaulay modules have eventually constant index of reducibility.

Characterizations of Gorenstein and Cohen-Macaulay rings via index of reducibility.

Provides new tools for analyzing module and ring properties through ideal invariants.

Abstract

It is shown that a module is sequentially Cohen-Macaulay if and only if the index of reducibility for distinguished parameter ideals are eventually constant with special value. As corollaries to the main theorem we given to characterize the Gorensteinness, Cohen-Macaulayness of local rings in term of eventually index of reducibility for distinguished parameter ideals.