On w-copure projective modules

Abstract

Let R be a commutative ring. An R-module M is said to be w-split if 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 Ext R 1 ( M , N ) (resp., Ext R n ( M , N ) ) is a GV-torsion R-module for all flat R-modules N and any n ≥ 1 .