n-gr-Coherent rings and Gorenstein graded modules

TL;DR

This paper introduces Ding n-gr-injective and Ding n-gr-flat modules over graded rings, explores their properties, and establishes their existence as covers and preenvelopes on n-gr-coherent rings, advancing the theory of Gorenstein graded modules.

Contribution

It defines new classes of modules in the context of graded rings and studies their properties and existence results, extending Gorenstein homological algebra.

Findings

Ding n-gr-injective and Ding n-gr-flat modules are characterized using finitely presented graded modules.

On n-gr-coherent rings, these modules admit covers and preenvelopes.

Relationships among these modules are established in the graded setting.

Abstract

Let R be a graded ring and n > 1 an integer. In this paper, We introduce the notions of Ding n-gr-injective and Ding n-gr-flat modules by using of special finitely presented graded modules . Then, some properties of Ding n-gr-injective and Ding n-gr-flat modules are obtained. On n-gr-coherent rings, we investigate the relationships among Ding n-gr-injective and Ding n-gr-flat modules and also, we prove that any graded module in R-gr (resp. gr-R) admits an Ding n-gr-injective (resp. Ding n-gr-flat) cover and preenvelope.