RINGS WHOSE SIMPLE MODULES ARE ABSOLUTELY PURE

Abstract

A ring is called right SAP if every right simple module over it is absolutely pure. In this paper we prove that every right SAP ring is semiprimitive and that the homomorphic image and the center of an right SAP ring are also right SAP. We also show that the sum of all absolutely pure minimal submodules of any module is a fully invariant submodule. As an application, we give a decomposition of some selfinjective rings.

ACKNOWLEDGMENT

We would like to thank Professor Ken Goodearl for his so much good advice concerning this paper. We would like to thank Professor Xu Yonghua for his constant inspiration and encouragement. We would also like to thank the anonymous referee for their valuble suggestions which help to improve the original presentation of this paper.