Amply Cofinitely Weak Essential Supplemented Modules

Abstract

In this work, amply cofinitely weak essential supplemented (briefly, amply cwe-supplemented) modules are defined and some properties of these modules are investigated. It is proved that every factor module and every homomorphic image of an amply cwe-supplemented module are amply cwe-supplemented. It is also proved that every ii-projective and cwe-supplemented module is amply cwe-supplemented. Let Lambda be any index set and {M lambda}Lambda be a family of projective R-modules. If M lambda is cwesupplemented for every lambda is an element of Lambda, then circle plus M lambda is amply cwe-supplemented. lambda is an element of Lambda Let M be a projective R-module. If M is cwe-supplemented, then every M-generated R-module is amply cwe-supplemented. Let R be any ring. Then every R-module is cwe-supplemented if and only if every R-module is amply cwe-supplemented.