International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 491-497

s-pure submodules

Iuliu Crivei

Department of Mathematics, Technical University of Cluj-Napoca, Str. C. Daicoviciu 15, Cluj-Napoca 400020, Romania

Received 23 September 2004; Revised 9 January 2005

Copyright © 2005 Iuliu Crivei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A submodule A of a right R-module B is called s-pure if fR1S is a monomorphism for every simple left R-module S, where f:AB 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.