Rings whose simple modules are absolutely pure

A ring is called right SAP if every right simple module over it is absolute ly 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 submod ules of any module is a fully invariant submodule. As an application, we gi ve a decomposition of some selfinjective rings.