MININJECTIVE AND MIN-CS-MODULES

Abstract

In this work, we study R-mininjective modules and introduce a generalization of R-mininjective, namely the concept of A-mininjective modules, where A is any module. We give different equivalent conditions for a module M to be mininjective. When M=M1ÅM2, we give a necessary and sufficient condition for M1 to be M2-mininjective. Finally, we study (S-R) bimodules SMR with the annihilator condition S=lS(A) + lS(B), where B is a complement of a simple submodule of MR and A is a closure of such a simple module. Such annihilator condition has a direct connection with the min-CS condition for MR. We make use of this to give a new characterization of min-CS-modules