当前位置:
X-MOL 学术
›
Georgian Math. J.
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
Notes on quasi-Frobenius rings
Georgian Mathematical Journal ( IF 0.8 ) Pub Date : 2021-02-01 , DOI: 10.1515/gmj-2019-2063 Zhanmin Zhu 1
Georgian Mathematical Journal ( IF 0.8 ) Pub Date : 2021-02-01 , DOI: 10.1515/gmj-2019-2063 Zhanmin Zhu 1
Affiliation
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.
中文翻译:
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。
更新日期:2021-03-16
中文翻译:
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。