模的弱消去问题与qu-正则环 |
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引用本文: | 武同锁. 模的弱消去问题与qu-正则环[J]. 数学学报, 1995, 38(6): 746-751 |
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作者姓名: | 武同锁 |
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作者单位: | 南京大学数学系,河北师范学院数学系 |
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摘 要: | 本文考虑模的弱消去问题与正则环的Stablerange条件,引进了qu-正则环的概念,并用它刻划了一类满足弱消去条件的模,刻划了qu-正则环,指出一切满足比较公理的正则环均为qu-正则环.文中还考虑这些结果的应用.例如,刻划了满足弱消去律的拟内射模;证明了素的正则右自内射环上的任意非奇异内射右R-模可以从直和项中弱消去.
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关 键 词: | 弱消去律,qu-正则环,自同态环,可比性,wsrl条件 |
收稿时间: | 1993-11-16 |
Weak Cancellation of Modules and qu-Regular Rings |
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Affiliation: | Wu Tongsuo(Nanjing University Nanjing 210008,China) |
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Abstract: | This paper studies weak cancellation of niodules and stable range condition of regularrings.We introduce the concept of qu-regular rings and apply it to characterizing a class ofmodules satisfying weak cancellation. We characterize qu-regular rings and indicate that allregular rings satisfying comparability axiom are qu-regular.We also consider the applicationsof these results,e.g.,we characterized quasi-injectiVe modules satisfying weak cancellation;weproved that every nonsingular injective right R-module over a prime,regular and right self-inective ring R can be weakly cancelled from direct summands. |
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Keywords: | weak cancellation qu-regular ring endomorphism ring wsrl condition |
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