提升模的无限直和

On Infinite Direct Sums of Lifting Modules

研究了提升模的任意直和在什么条件下仍是提升模.例如证明了M=i∈IMi是提升模当且仅当存在i∈I,对M的任意余闭子模K,若M=K+M-i,则K是M的直和项,或者Mi在M中的任意补P是M的直和项且M/P是提升模.

When a direct sum of lifting modules is lifting is studied here. For example, it is proved that the direct sum M=（＋）i∈IMi is lifting if and only if there exists i∈I such that very coclosed submodule K of M with M=K＋M-i is a direct summand, or every supplement P of Mi in M is a direct summand and M/P is lifting.