PSD-补模

PSD-supplemented modules

设R是环,M是右R-模.称模M为PSD-补模,如果对于M的任意子模N,存在M的子模K,使得M=N+K且N∩K在K中是PSD的.给出PSD-补模的一些性质,证明对于duo-模M=M1M2,如果M1,M2是PSD-补模,则M是PSD-补模.

Let R be a ring and M an right R-module. M is called PSD-supplemented module if for every submodule N of M, there is a submodule K of M such that M= N＋K and Nr）K is PSD in K. Some prop- erties of PSD-supplemented modules were given and it was proved that a duo-module M=M1○M2 would be a PSD-supplemented module if M1 and M2 were PSD-supplemented modules.