| 极大-内射环上的一些注记(英文) |
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| 引用本文： | 汪明义,罗荣. 极大-内射环上的一些注记(英文)[J]. 四川师范大学学报(自然科学版), 2012, 35(3): 331-334 |
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| 作者姓名： | 汪明义 罗荣 |
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| 作者单位： | 1. 宜宾学院数学系 四川宜宾644000
2. 西南交通大学数学学院 四川成都610031 |
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| 基金项目： | 国家自然科学基金，中央高校基本科研业务费专项基金 |
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| 摘 要： | 设R是一个环.在文献(M.Y.Wang,G.Zhao.Acta Mathematica Sinica,2005,21:1451-1458.)中,如果从环R的任意右理想到R自身的每个态射都能被表示成为R中的某个元素左乘形式,那么该环R被称为右极大-内射环.给出了V-环、半单环的等价刻划;并证明了如果一个凝聚-SF环R是余挠的,那么R是极大-内射的;以及表明了极大-内射环的存在性:极大-内射生成子的自同态环是极大-内射的.最后,证明了一个右极大-内射左完全环R是quasi-Frobenius环当且仅当它满足左W-条件.
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| 关 键 词： | 极大内射性 拟-Frobenius环 余挠模 W-条件 |
Some Notes on Max-injective Rings |
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| WANG Ming-yi , LUO Rong. Some Notes on Max-injective Rings[J]. Journal of Sichuan Normal University(Natural Science), 2012, 35(3): 331-334 |
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| Authors: | WANG Ming-yi LUO Rong |
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| Affiliation: | 1.Department of Mathematics,Yibin University,Yibin 644000,Sichuan;2.College of Mathematics,Southwest Jiaotong University,Chengdu 610031,Sichuan) |
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| Abstract: | Let R be a ring.From M.Y.Wang and G.Zhao(Acta Mathematica Sinica,2005,21: 1451 1458.),we know that R is said to be right max-injective in case every homomorphism from any right maximal ideal to R can be represented as a left multiplication by an element of R.In this paper,we give some equivalent conditions of V-rings and semi-simple rings,and show that a coherent SF-ring R is max-injective if it is cotorsion.And then,we obtain the existence of max-injective rings: the endomorphism ring of a max-injective generator is max-injective.Finally,we prove that a right max-injective left perfect ring R is quasi-Frobenius if and only if R satisfies the left W-condition. |
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| Keywords: | maximal injectivity quasi-Frobenius rings cotorsion modules W-conditions |
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