| SF'-环的正则性 |
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| 引用本文： | 方霞,肖光世.SF'-环的正则性[J].宝鸡文理学院学报(自然科学版),2008,28(2). |
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| 作者姓名： | 方霞 肖光世 |
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| 作者单位： | 南京航空航天大学,理学院,江苏,南京,210016 |
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| 摘 要： | 目的 环R的每一个单奇异的左(右)R-模是平坦的,则称R是左(右)SF'-环,文章研究SF'-环的正则性.方法 在幂等元是左半中心的和LANE-环的条件下讨论SF'-环.结果 得到了SF'-环是强正则环的两个充要条件:(1)R是左SF'-环,如果R/Z(RR)是约化的,则R是强正则环;(2)R是强正则环当且仅当R是满足幂等元左半中心的左SF'-环,且R是LANE-环.结论 这些结果对于解决SF-环是否是正则环有一定意义.
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| 关 键 词： | 强正则环 SF'-环 SF-环 |
The regularity of SF'-rings |
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| FANG Xia,XIAO Guang-shi.The regularity of SF'-rings[J].Journal of Baoji College of Arts and Science(Natural Science Edition),2008,28(2). |
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| Authors: | FANG Xia XIAO Guang-shi |
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| Abstract: | Aim A ring R is a left(right) SF'-ring if every simple singular left(right) R-module is flat.The regularity of SF'-rings is studied.Methods SF'-rings are discussed on condition that every idempotent element is left semi-center and SF'-rings are LANE-ring.Results Two new characterizations of regular rings are given.(1) If R is a left SF'-ring and R/Z(RR) is reduced,then R is strongly regular;(2) R is strongly regular if and only if R is a left SF'-ring whose every idempotent element of R is left semi-center and is LANE-ring.Conclusion The results are helpful for the problem that SF-rings are regular rings or not. |
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| Keywords: | strongly regular rings SF'-rings SF-rings |
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