On G-$(n,d)$-rings

TL;DR

This paper introduces and studies a new class of rings called G-(n,d)-rings, where modules have bounded Gorenstein projective dimension, and characterizes specific cases like n-coherent G-(n,0)-rings with examples.

Contribution

It defines G-(n,d)-rings, explores their properties, and characterizes n-coherent G-(n,0)-rings, expanding the understanding of Gorenstein homological dimensions in ring theory.

Findings

Characterization of n-coherent G-(n,0)-rings

Introduction of G-(n,d)-ring class

Examples illustrating G-(n,d)-rings

Abstract

The main aim of this paper is to investigate new class of rings called, for positive integers $n$ and $d$, $G-(n,d)-$rings, over which every $n$-presented module has a Gorenstein projective dimension at most $d$. Hence we characterize $n$-coherent $G-(n,0)-$rings. We conclude by various examples of $G-(n,d)-$rings.