On the reduced grades of modules over commutative rings

TL;DR

This paper refines previous results on the reduced grade of modules over commutative Noetherian rings, removing certain assumptions and broadening the applicability of the theory.

Contribution

It significantly improves existing theorems by eliminating the need for modules to be horizontally linked or have finite GC-dimension.

Findings

Refined theorems on reduced grade of modules

Removed assumptions of horizontal linkage and finite GC-dimension

Broadened understanding of module properties over commutative rings

Abstract

Let R be a commutative Noetherian ring. Recently, Dibaei and Sadeghi have studied the reduced grade of a horizontally linked R-module M of finite GC-dimension, where C is a semidualizing R-module. In this paper, we highly refine their results. In particular, our main result removes the assumptions that M is holizontally linked and M has finite GC -dimension.