Some new Subcategories and homological dimensions related to Semidualizing modules

TL;DR

This paper introduces new classes of modules and homological dimensions based on semidualizing modules over Noetherian rings, exploring their properties and conditions for dualizing modules.

Contribution

It defines and studies novel module classes and homological dimensions using semidualizing modules, providing new insights into their structure and duality conditions.

Findings

New classes of modules related to semidualizing modules

Characterization of dualizing modules via homological conditions

Relations between homological dimensions and module properties

Abstract

Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the semidualizing modules, we define and study new classes of modules and homological dimensions and investigate the relations between them. In parallel, we obtain some necessary and sufficient condition for $ C $ to be dualizing.