On w-copure projective modules

Abstract

Let R be a commutative ring. An R-module M is said to be w-split if ${\text{Ext}}_R^1(M,N)$ is a GV-torsion R-module for all R-modules N. It is known that every projective module is w-split, but the converse is not true in general. In this paper, we study the w-split dimension of a flat module. To do so, we introduce and study the so-called w-copure (resp., strongly w-copure) projective modules, which is in some way a generalization of the notion of copure (resp., strongly copure) projective modules. An R-module M is said to be w-copure projective (resp., strongly w-copure projective) if ${\text{Ext}}_R^1(M,N)$ (resp., ${\text{Ext}}_R^n(M,N)$) is a GV-torsion R-module for all flat R-modules N and any $n\ge 1$.

KEYWORDS:

• Copure projective
• DW rings and domains
• Krull domains
• w-projective
• w-split

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13D05
• 13D07
• 13H05