The projectively resolving of some classes over a direct product of rings

TL;DR

This paper investigates the properties of strongly Gorenstein projective and flat modules over a direct product of commutative rings, expanding understanding of module resolution in algebraic structures.

Contribution

It introduces methods to resolve these classes of modules specifically over direct products of rings, a novel approach in the context of Gorenstein homological algebra.

Findings

Characterization of strongly Gorenstein projective modules over product rings

Resolution techniques for strongly Gorenstein flat modules

Extension of Gorenstein homological properties to product rings

Abstract

In this paper, we study the resolving of $\mathcal{SGP}(-)$ and $\mathcal{SGF}(-)$, the classes of all strongly Gorenstein projective and flat modules respectively, over a direct product of commutative rings.