On the decomposition of noncosingular $\sum$-lifting modules

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.‎‎