ON fPP—Rings |
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引用本文: | 杜先能,章聚乐.ON fPP—Rings[J].数学季刊,1993,8(1):77-80. |
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作者姓名: | 杜先能 章聚乐 |
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摘 要: | in this psper,we investigate nore general rings than GPP-rings,called fPP-rings.First,we in-vestigate fPP-rings and their classical quotient quotient rings.We ptove (1) fPP-rings are f-quasi-regular rings.(2)R is a fPP-ring then Q(R) is fPP-ring.(3)R= iRi is a fPP-ring if and only if every Ri is a fPP-ring.Second,we present a characterization of fPP-ring via fP-injectivity,we prove that R is a fPP-ring if and only if every quotient module of a imjective R-module is fP-injectiv if and only ifevery quotient module of a P-injective R-module is fP-injective.Third,we study how fPP-rings are related to von Neu-mann regular rings,we prove that R is von Nevmann regular if and only if R is fPP-ring and for every α∈R,there is b∈E(R) and d∈R suth that α=f(α)b and f(α)=f^2(α) d for some f∈F(R).Finally,we give a example of fPP-ring which is not GPP-ring.
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关 键 词: | fPP环 GPP环 商环 f拟正则环 fP单射 可交换环 非零因子 |
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