| EIFP环 |
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| 引用本文： | 胡雅蓉,李男杰,魏俊潮.EIFP环[J].扬州大学学报(自然科学版),2012,15(2):6-8,16. |
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| 作者姓名： | 胡雅蓉 李男杰 魏俊潮 |
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| 作者单位： | 扬州大学数学科学学院,江苏扬州,225002 |
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| 基金项目： | 国家自然科学基金资助项目，江苏省高校自然科学基金资助项目 |
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| 摘 要： | 给出EIFP环的定义,研究EIFP环的一些性质.主要证明了如下结果:①设R为EIFP环,则对每个e∈E(R),有eR(1-e)■J(R);②设R为quasi-normal环,e∈E(R),则R是EIFP环当且仅当eRe及(1-e)R(1-e)都是EIFP环;③R是Abel环当且仅当R是EIFP环和强左幂等自反环;④R是强正则环当且仅当R是von Neumann正则环和EIFP环;⑤R是约化环当且仅当R是n-正则环和EIFP环;⑥EIFP的exchange环有稳定域1.
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| 关 键 词： | EIFP环 幂等元 Abel环 von Neumann正则元 稳定域1 |
EIFP rings |
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| HU Ya-rong
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LI Nan-jie
,
WEI Jun-chao.EIFP rings[J].Journal of Yangzhou University(Natural Science Edition),2012,15(2):6-8,16. |
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| Authors: | HU Ya-rong LI Nan-jie WEI Jun-chao |
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| Institution: | (Sch of Math Sci,Yangzhou Univ,Yangzhou 225002,China) |
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| Abstract: | In this paper,the author introduces the notion of EIFP rings and studies some properties of EIFP rings.The following results are obtained:① Let R be a EIFP ring and e∈E(R).Then eR(1-e)■J(R);② Let R be a quasi-normal ring and e∈E(R).Then R is a EIFP ring if and only if eRe and(1-e)R(1-e) are all EIFP rings;③ R is an Abelian ring if and only if R is a EIFP ring and strongly left idempotent reflexive ring;④ R is a strongly regular ring if and only if R is a von Neu-mann regular ring and EIFP ring;⑤ R is a reduced ring if and only if R is a n-regular ring and EIFP ring;⑥ EIFP exchange rings have stable range 1. |
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| Keywords: | EIFP rings idempotent elements Abel rings von Neumann regular elements stable range 1 |
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