| 章聚乐.p-内射性与Artin半单环(英文)[J].数学研究及应用,1991,11(4):579~585 |
| p-内射性与Artin半单环(英文) |
| p-Inj ectivity and Artinian Semisimple Rings |
| 投稿时间：1989-11-23 |
| DOI：10.3770/j.issn:1000-341X.1991.04.023 |
| 中文关键词: |
| 英文关键词: |
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| 中文摘要: |
| P-内射性在环论研究中有独特的作用,并且越来越被人们所重视.本文的目的是利用p-内射性来刻化Artin半单环,我们得到如下主要结果:(1)环R是Artin半单的当且仅当R是p-内射的,R的左奇异理想是闭右理想,且R满足特殊左零化子升链条件;(2)环R是Artin半单的当且仅当R的每个极大本质左理想是左零化子,并且任意奇异单左R-模是p-内射的;(3)素环R是Artin单的当且仅当R的右基层S≠0是左p-内射的,并且R满足特殊左零化子升链条件.这些结果不仅加深了对Artin半单环的认识,而且建立了半单环与某 |
| 英文摘要: |
| Since several years, Artinian semisirnple rings have drawn the attention of various authors (cf. for example, [l]-[10]). The purpose of this paper is to characterize Artinian semisimple rings in terms of P- in jectivity. New characteri-zations of Artinian semisimple rings are obtained. Necessary and sufficient con-ditions for prime rings to be Artinian simple are given. Several interesting pro-perties of P- injective rings are derived. |
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