On Generalizations of PF-Rings
On Generalizations of PF-Rings
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DOI：
10.1081/agb-120027909
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发表时间：
2004-03
影响因子：
0.7
通讯作者：
Jianlong Chen;Nanqing Ding;M. Yousif
中科院分区：
文献类型：
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作者：
Jianlong Chen;Nanqing Ding;M. Yousif
如果环R是具有本质右凸的半完全右单射环，则称为右wpf环（弱pf环）。右wpf环的种类比右pf环的种类更广。在本文中，我们研究并给出了这类新环的几个表征。我们还证明了如果R是一个左完备，左右f内射环，那么R是QF当且仅当So c2 (R)是一个有限生成的右R模当且仅当R/Soc(R)是一个有限共生的左R模。一些已知的结果作为推论得到。
Abstract A ring R is called a right WPF-ring (weak PF-ring) if R is a semiperfect right simple-injective ring with essential right socle. The class of right WPF-rings is broader than that of right PF-rings. In this article, we study and provide several characterizations of this new class of rings. We also show that if R is a left perfect, left and right f-injective ring, then R is QF if and only if So c 2(R) is a finitely generated right R-module if and only if R/Soc(R) is a finitely cogenerated left R-module. Some known results are obtained as corollaries.