We give some new characterizations of quasi-Frobenius rings. Namely, we prove that for a ring R , the following statements are equivalent: (1) R is a quasi-Frobenius ring, (2) M2⁢(R){M_{2}(R)} is right Johns and every closed left ideal of R is cyclic, (3) R is a left 2-simple injective left Kasch ring with ACC on left annihilators, (4) R is a left 2-injective semilocal ring such that R/Sl{R/S_{l}} is left Goldie, (5) R is a right YJ-injective right minannihilator ring with ACC on right annihilators.

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关于准Frobenius环的注释

我们给出了准Frobenius环的一些新特征。即，我们证明对于环R，以下陈述是等价的：（1）R是一个准弗罗宾尼斯环，（2）M2⁢（R）{M_ {2}（R）}是正确的约翰斯且每个闭合R的左理想是循环的，（3）R是在左an灭子上带有ACC的左2个单射左Kasch环，（4）R是一个左2射半半环，使得R / Sl {R / S_ {l }}是左边的Goldie，（5）R是在右-灭子上带有ACC的右YJ注入右right灭子环。