C11 -modules via left exact preradicals

Abstract

In this article, we study modules with the condition that every image of a submodule under a left exact preradical has a complement which is a direct summand. This new class of modules properly contains the class of $C_{11}$-modules (and hence also $CS$-modules). Amongst other structural properties, we deal with direct sums and decompositions with respect to the left exact preradicals of this new class of modules. It is obtained a decomposition such that the image of the module itself is a direct summand for the left exact radical, which enjoys the new condition.