Strongly injective modules
Let \(R\) be a ring with unity and \(M\) be a left \(R\)-module. In this paper, a module \(M\) is called strongly injective if whenever \(M+K=N\) with \(M\leq N\), there exists \(L\leq K\) such that \(M\oplus L=N\). Then the authors show that a module is strongly injective if and only if it is semisimple and injective. Further, new characterizations of left V-rings and semisimple rings are given via strongly injective modules. In particular, it is shown that \(R\) is a left V-ring if and only if every Artinian left \(R\)-module is strongly injective. Also it is shown that a ring \(R\) is semisimple if and only if every left \(R\)-module is strongly injective.
scientific article; zbMATH DE number 7343247
scientific article