THE INVARIANT PROPERTIES ON THE CS-MODULES AND APPLICATIONS

Abstract

In this paper, we prove some invariant properties on the CS-module and application. We also prove some preserving correspondences of closed submodules, and then apply it to transfer the CS, max CS, min CS, max-min CS and (strongly) FI-extending properties of a module to its endomorphism ring. Endomorphism rings of modules with Baer and Rickart properties are studied. Furthermore, the right-left symmetry of Goldie, CS and max-min CS conditions on the endomorphism rings of prime and semiprime modules are investigated. Some examples are discussed to guarantee that our main results make sense.