ON ZM-SEMIPERFECT MODULES

Abstract

Let τM be any preradical for σ[M] and N any module in σ[M]. N is

called a τM -semiperfect module if for every submodule K of N , there is a

decomposition K = A⊕B such that A is a projective direct summand of

N in σ[M] and B ⊆ τM(N). In this paper we prove that any finite direct

sum of τM -semiperfect modules is τM -semiperfect. It is also shown that

if M is a local projective module in σ[M], then for every index set Λ, the (Λ)

sum M is ZM-semiperfect in σ[M] if and only if every factor module

of M

(Λ)

has a projective ZM -cover.