Gorenstein projective precovers

TL;DR

This paper establishes that Gorenstein projective modules form a special precovering class over certain rings, expanding understanding of their structure and providing examples beyond traditional classes.

Contribution

It proves the precovering property of Gorenstein projective modules over a broad class of rings including Gorenstein, noetherian, and n-perfect rings, with new examples.

Findings

Gorenstein projective modules are special precovering over left GF-closed rings.

Includes rings where Gorenstein flat modules have finite Gorenstein projective dimension.

Provides examples of rings with these properties that are not right coherent.

Abstract

We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In section 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.