Auslander class, $\g_C$ and $C$--projective modules modulo exact zero-divisors

TL;DR

This paper investigates various module classes related to semidualizing modules over rings, focusing on their properties and relationships modulo exact zero-divisors, expanding the understanding of homological dimensions.

Contribution

It introduces and analyzes the behavior of Auslander, Bass, and related classes of modules in the context of exact zero-divisors, providing new insights into their structure and dimensions.

Findings

Characterization of module classes modulo zero-divisors

Relationships between different homological dimensions

Extensions of classical module theory results

Abstract

For a semidualizing module $C$ over a ring $R$, we study the following classes modulo exact zero divisors: $\g_C$--projectives, $\mathcal G_C$; the Auslander class $\mathcal A_C$; the Bass class $\mathcal B_C$; $\mathcal{P}_C$--projective; $ {\mathcal F}_C$--projective; and ${\mathcal I}_C$--injective dimensions.