ON NON-?-M-COSINGULAR COMPLETELY ?-?M-SUPPLEMENTED MODULES

Abstract

In this paper we prove that any circle plus-delta(M)-supplemented module N is an element of sigma [M] with SSP is completely circle plus-delta(M)-supplemented. It is also proved that any non-delta-M-cosingular circle plus-delta(M)-supplemented module N is an element of sigma [M] is (D-3) if and only if N has the SIP. Let N is an element of sigma [M] be any module such that (Z) over bar delta(M) (N) has a coclosure in N. Then we prove that N is (completely) circle plus-delta(M)-supplemented if and only if N = (Z) over bar (2)(delta M) (N) circle plus K for some submodule K of N such that (Z) over bar (2)(delta M) (N) and K both are (completely) circle plus-delta(M)-supplemented.