Characterizations of QF Rings |
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| Authors: | Jianlong Chen Liang Shen Yiqiang Zhou |
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| Institution: | 1. Department of Mathematics , Southeast University , Nanjing, China jlchen@seu.edu.cn;3. Department of Mathematics , Southeast University , Nanjing, China;4. Department of Mathematics and Statistics , Memorial University of Newfoundland , St. John's, Canada |
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| Abstract: | A ring R is called “left GP-injective” if for any 0 ≠ a ∈ R, there exists n > 0 such that a n ≠ 0 and a n R = r(l(a n )). It is proved that (1) every right Noetherian left GP-injective ring such that every complement left ideal is a left annihilator is a QF ring, (2) every left GP-injective ring with ACC on left annihilators such that every complement left ideal is a left annihilator is a QF ring, and (3) every left P-injective left CS ring satisfying ACC on essential right ideals is a QF ring. Several well-known results on QF rings are obtained as corollaries. |
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| Keywords: | CS rings GP-injective rings P-injective rings QF rings |
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