Mininjective and min-CS-modules. (Q928520)

Let \(R\) be a ring and \(M,A\) be right \(R\)-modules. Then \(M\) is called: (i) \(A\)-mininjective if for every simple submodule \(K\) of \(A\), every homomorphism \(f\colon K\to M\) can be extended to \(A\); (ii) min-CS-module if every simple submodule of \(M\) is essential in a direct summand of \(M\). The authors establish several properties and characterizations of \(R\)-mininjective modules and min-CS-modules. For instance, when \(M=M_1\oplus M_2\), they give a necessary and sufficient condition for \(M_1\) to be \(M_2\)-mininjective. They also relate min-CS-modules with some annihilator conditions.