Gorenstein n-X-injective and n-X-flat modules with respect to a special finitely presented module

TL;DR

This paper introduces new classes of Gorenstein n-X-injective and n-X-flat modules using special finitely presented modules, explores their properties on n-X-coherent rings, and generalizes existing results in the context of X-FC-rings.

Contribution

It defines Gorenstein n-X-injective and n-X-flat modules via special finitely presented modules and studies their properties and relations on specific ring classes, extending prior results.

Findings

Characterization of Gorenstein n-X-injective and n-X-flat modules

Equivalent properties on n-X-coherent rings

Relations among various module classes on X-FC-rings

Abstract

Let R be a ring, X a class of R-modules and n>1 an integer. In this paper, via special finitely presented modules, we introduce the concepts of Gorenstein n-X-injective and n-X-flat modules. And aside, we obtain some equivalent properties of these modules on n-X-coherent rings. Then, we investigate the relations among Gorenstein n-X-injective, n-X-flat, injective and flat modules on X-FC-rings (i.e., self n-X-injective and n-X-coherent rings). Several known results are generalized to this new context