$(n,m)$-SG rings

TL;DR

This paper introduces and explores a new class of rings called $(n,m)$-SG rings, characterized by finite Gorenstein global dimension, expanding the understanding of ring structures in algebra.

Contribution

It defines the $(n,m)$-SG rings, provides examples for specific parameters, and extends the theory of rings with finite Gorenstein global dimension.

Findings

Introduction of $(n,m)$-SG rings concept

Examples for $n=1,2$ and all $m extgreater{}0$

Extension of Gorenstein global dimension theory

Abstract

This paper is a continuation of the paper Int. Electron. J. Algebra 6 (2009), 219-227. Namely, we introduce and study a doubly filtered set of classes of rings of finite Gorenstein global dimension, which are called $(n,m)$-SG for integers $n\geq 1$ and $m\geq 0$. Examples of $(n,m)$-SG rings, for $n=1$ and 2 and every $m\geq 0$, are given.