International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 491-497
doi:10.1155/IJMMS.2005.491

s-pure submodules

Abstract

A submodule A of a right R-module B is called s-pure if f⊗R1S is a monomorphism for every simple left R-module S, where f:A→B is the inclusion homomorphism. We establish some properties of s-pure submodules and use s-purity to characterize commutative rings with every maximal ideal idempotent.