Department of Mathematics, Quchan University of Advanced Technology, Quchan, Iran.
Abstract
Let $R$ be a right artinian ring or a perfect commutative ring. Let $M$ be a noncosingular self-generator $\sum$-lifting module. Then $M$ has a direct decomposition $M=\oplus_{i\in I} M_i$, where each $M_i$ is noetherian quasi-projective and each endomorphism ring $End(M_i)$ is local.
)