SS-Supplemented Modules

Abstract

Amodule M is called ss-supplemented if every submodule U of M has a supplement V in M such that U \\ V is semisimple. It is shown that a Önitely generated module M is ss-supplemented i§ it is supplemented and Rad(M ) Soc(M ). A module M is called strongly local if it is local and Rad(M ) is semisimple. Any direct sum of strongly local modules is ss- supplemented and coatomic. A ring R is semiperfect and Rad(R) Soc(RR) i§ every left R-module is (amply) ss-supplemented i§ RR is a Önite sum of strongly local submodules.