摘要
本文将正则环的一些性质推广到模中,得到如下主要结果:1.设M是R-模,N是M的S-R-子模。则M是正则的当且仅当(1)M是局部投影的;(2)N是M的正则子模;(3)M/N是正则的R/Ann_R(M/N)-模。2.R-模M是正则的当且仅当(1)M是局部投影的;(2)M是半素;(3)M的半素S-R-子模升链的并仍是半素的;(4)对于M的任意素S-R-子模N,M/N是正则的R/Ann_R(M/N)-模。
In this paper,we give following characterzations of regular modules: 1.Let M be a R-module and N be a S-R-submodule of M.M is regular if and only if (1)M is locally projective; (2)N is regular submodules of M; (3)M/N is regular R/AnnR(M/N)-module. 2.R-module M is regular if and only if (1)M is locally Projective; (2)M is semiprime; (3)The Union of ascending chain of semiprime S-R-submodules is semiprime; (4)For every prime S-R-submodule N of M,M/N is regular R/AunR(M/N) -module.
关键词
正则环
正则模
局部投影模
素子模
(Von Neumann)Regular ring
Regular module
Locally projective module
Prime submodule
Semiprime submodule
