RINGS OVER WHICH EVERY MODULE IS ALMOST INJECTIVE

摘要

We study the rings R for which every R-module is almost injective. For such a ring R, it is shown that R/Soc (R-R) is semisimple and Rad(R) is finitely generated. It is proved that these rings are exactly Artinian serial rings with Rad(R)(2) = 0, if one of these conditions hold: Soc(R-R) is finitely generated, R-R is extending, R is semiperfect or R is of finite reduced rank.