ON NON-o-M-COSINGULAR COMPLETELY-o_M-SUPPLEMENTED MODULES

摘要

In this paper we prove that any -o_M-supplemented module N E a[M] withSSP is completely -o_M-supplemented. It is also proved that any non-o-M-cosingular -o_M-supplemented module N E a[M] is (D3) if and only if N hasthe SIP. Let N E a[M] be any module such that Zo_M(N) hasa coclosure inN. Then we prove that N is (completely)-o_M-suppleme nt e d if and only ifN = Z_(oM)~2(N) Kfor some submoduleKofNsuch that Z_(o_M)~2(andKbothare (completely) -o_M-supplemented.