摘要
作为弱补模的真推广,引入K-弱补模的概念并给出K-弱补模的基本性质.证明K-弱补模的任意直和项是K-弱补模.设M=in=1Mi,Mi(i=1,2,…,n)是M的完全不变子模.若Mi(i=1,2,…,n)是K-弱补模,则M是K-弱补模.设R是环.若J(R)=0,则RR是K-弱补模当且仅当R是左PP-环.
As a proper generalization of weakly supplemented modules, the concept of к-weakly supplemented modules was introduced and their basic properties were given. It was proved that any direct summand of a к-weakly supplemented module was к-weakly supplemented. Let M=i^n=iMi be a direct sum of fully invariant submodules Mi （i= 1,2,… ,n）. If Mi was X-weakly supplemented, then M was к-weakly supplemented. Let R be a ring with J（R）=0. Then RR was a к-weakly supplemented module if and only if R was a left PP-ring.
出处
《兰州理工大学学报》
CAS
北大核心
2007年第6期126-127,共2页
Journal of Lanzhou University of Technology
关键词
弱补模
к-弱补模
完全不变子模
weakly supplemented modules
N-weakly supplemented modules
fully invariant submodules
