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| DI-环的一些性质 | |
| 引用本文： | 杜奕秋. DI-环的一些性质[J]. 松辽学刊, 2005, 26(4): 75-76,78 |
| 作者姓名： | 杜奕秋 |
| 作者单位： | 吉林师范大学数学学院,吉林四平136000 |
| 摘 要： | 本文定义并研究了DI-环，得到如下结果：1．若环R可换，则R是DI-环〈=〉是Hereditary-环和Noether-环；2．给出了DI-环R本身所具有的三个性质；3．研究了DI-环与V-环，QI-环，QF-环以及正则环的关系． |
| 关 键 词： | Hereditary-环 Noether-环 内射模 可除模 |
| 文章编号： | 1000-1840-（2005）04-0075-02 |
| 收稿时间： | 2005-07-21 |
| 修稿时间： | 2005-07-21 |
DI- ring |
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| DU Yi-qiu. DI- ring[J]. Songliao Journal (Natural Science Edition), 2005, 26(4): 75-76,78 | |
| Authors: | DU Yi-qiu |
| Affiliation: | College of Mathematics,Jilin Normal University,Siping 136000,China |
| Abstract: | We consider in this paper rings in which every divisible R - module is injective. These rings will be referred to as DI - rings. The object of this paper is to prove theoreml: Commutative ring R is DI - ring if and only if R is Hereditary - ring and Noether-ring. We give some characters of DI - ring and discuss relation of DI - ring with V - ring, QI - ring, QF - ring, Riguular - ring. |
| Keywords: | Hereditary - ring N oether - ring injective model divisible model |
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