Abstract
We study the rings R for which every R-module is almost injective. For such a ring R, it is shown that R/Soc(RR) 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(RR) is finitely generated, RR is extending, R is semiperfect or R is of finite reduced rank.
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