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 certainconditions (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 onthe endomorphism rings of max-min CS modules is investigated.