WHEN CF RINGS ARE ARTINIAN
WHEN CF RINGS ARE ARTINIAN
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DOI：
10.1142/s0219498812500594
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发表时间：
2013-03
影响因子：
0.8
通讯作者：
Wenxi Li;Jianlong Chen
中科院分区：
文献类型：
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作者：
Wenxi Li;Jianlong Chen
设R是一个环，如果每个元素的右零子在R的直接被加数中是必需的，则R称为右ACS环。我们证明右CF环在右ACS条件下是右artinian。特别是，FGF猜想在正确的ACS条件下是正确的。我们还给出了右诺特左P-内射和左ACS环为QF的一些条件。
Let R be a ring, R is called a right ACS ring if the right annihilator of each element is essential in a direct summand of R. We prove that right CF ring is right artinian under right ACS condition. In particular, FGF conjecture is true under right ACS condition. We also give some conditions under which right noetherian left P-injective and left ACS ring is QF.