| 正则模的几个特征性质 |
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| 引用本文： | 张远平. 正则模的几个特征性质[J]. 安徽师范大学学报(自然科学版), 1991, 14(3): 10-14 |
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| 作者姓名： | 张远平 |
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| 作者单位： | 安徽师大数学系 |
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| 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。
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| 关 键 词： | 正则环 正则模 局部投影模 素子模 |
Some Characterizations of Regular Modules |
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| Zhang Yuanping. Some Characterizations of Regular Modules[J]. Journal of Anhui Normal University(Natural Science Edition), 1991, 14(3): 10-14 |
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| Authors: | Zhang Yuanping |
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| Affiliation: | Zhang Yuanping Department of Mathematics |
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| Abstract: | 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. |
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| Keywords: | (Von Neumann)Regular ring Regular module Locally projective module Prime submodule Semiprime submodule |
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