On rings with cyclic almost-injective modules

Abstract

It is shown that every finitely generated right R-module is almost injective if and only if every cyclic right R-module is almost injective, if and only if R/J(R) is a right SV-ring with Loewy(RR) ≤ 2 and there is a finite set of orthogonal idempotents {ei}i I in R such that eiR is an injective local right R-module of length two for every i I and J(R) = i IJ(eiR).