The Right Orthogonal Class $\GP(R)^{\perp}$ via $\Ext$

TL;DR

This paper investigates the properties of Gorenstein projective modules and their orthogonal complements, establishing conditions for cotorsion theory completeness and exploring relationships with Gorenstein flat modules.

Contribution

It proves the completeness and hereditary nature of the cotorsion theory for Gorenstein projective modules under finite Gorenstein global dimension.

Findings

Cotorsion theory for Gorenstein projective modules is complete and hereditary when $l. ext{Ggldim}(R)<inite$

Conditions under which Gorenstein projective modules are Gorenstein flat are discussed

Provides new insights into the structure of Gorenstein modules and their orthogonal classes.

Abstract

In this paper, we study the pair $(\GP(R),\GP(R)^{\perp})$ where $\GP(R)$ is the class of all Gorenstein projective modules. We prove that it is complete hereditary cotorsion theory provided $l.\Ggldim(R)<\infty$. We discuss also, when every Gorenstein projective module is Gorenstein flat.