Max CS and min CS modules

Abstract

In this work, we study max CS, min CS, max-min CS modules and their endomorphism rings. Under certain conditions e.g., related to nonsingularity and duo-ness , we prove that a module is max CS if and only if it is min CS, and that direct sums of min max CS modules is again min max CS. Finally, symmetry of max-min CS property on the endomorphism rings of max-min CS modules is investigated.