| 4-IF环的刻画 |
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| 引用本文： | 张友,刘红梅. 4-IF环的刻画[J]. 大连民族学院学报, 2013, 15(5): 516-517,521 |
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| 作者姓名： | 张友 刘红梅 |
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| 作者单位： | 大连民族学院理学院,辽宁大连,116605 |
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| 摘 要： | 引入了A-内射模和A-平坦模的定义，由此构造了A-伊环，利用平坦模和内射模给出了A-伊环的8个等价命题，得到了环R分别是伊环、A-正则环和正则环的充要条件，即：R是伊环，当且仅当只是A-伊环且A-平坦模的每个内射子模是平坦模；环R是A-正则环，当且仅当R是A-伊环且A-平坦模的子模是A-平坦模；环R是正则环，当且仅当R是A-伊环且A-平坦模的子模是平坦模。
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| 关 键 词： | 平坦模 内射模 A-IF环 |
Characterization of A-IF Ring |
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| ZHANG You , LIU Hong-mei. Characterization of A-IF Ring[J]. Journal of Dalian Nationalities University, 2013, 15(5): 516-517,521 |
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| Authors: | ZHANG You LIU Hong-mei |
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| Affiliation: | ZHANG You, LIU Hong - mei (College of Science, Dalian Nationalities University,Dalian Liaoning 116605, China) |
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| Abstract: | It is aimportant method that rings are characterized by modules. In this paper we intro- duce the definition of A - injective mould and A - fiat mould, and then we construct A - IF ring. We gave eight equivalent propositions of A - IF ring by injective modules and fiat modules, and obtain the necessary and sufficient conditionof R for A - IF ring, A - regular ring and regu- lar ring. That is that ring R is IF ring if and only if R is A - IF ring and any injective sub - mod- ule of A - fiat module is fiat module ; Ring R is A - regular ring if and only if R is A - IF ring, and any sub - module of A - fiat module is A - fiat module ; Ring R is regular ring if and only if R is A - IF ring, and any sub - module of A - fiat module is fiat module. |
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| Keywords: | flat modules injective modules A - IF ring |
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