平凡环扩张上的强Ding投射模

Strongly Ding Projective Modules over Trivial Ring Extensions

设R■M是平凡环扩张,其中R是环,M是(R,R)-双模.在特定条件下,证明(X,α)是强Ding投射左R■M-模当且仅当序列■正合,并且coker(α)是强Ding投射左R-模.

Let R■M be a trivial ring extension,where R be a ring,M be an(R,R)-bimodule.We prove that(X,α)is a strongly Ding projective left R M-module if and only if the sequence M■R M■RX M■αM■RXα→X is exact and coker(α)is a strongly Ding projective left R-module under certain conditions.