Prethick subcateogries of modules and characterizations of local rings

TL;DR

This paper introduces prethick subcategories to characterize local rings via homological dimensions, providing new tools that recover existing theorems and deepen understanding of local ring structures.

Contribution

The paper introduces the concept of prethick subcategories and uses them to characterize local rings, extending previous results in homological algebra.

Findings

Recovered theorems of Salarian, Sather-Wagstaff, and Yassemi

Introduced prethick subcategories as a new tool

Provided new characterizations of local rings

Abstract

This paper studies characterizing local rings in terms of homological dimensions. The key tool is the notion of a prethick subcategory which we introduce in this paper. Our methods recover the theorems of Salarian, Sather-Wagstaff and Yassemi.