| Clean环及其扩张 |
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| 引用本文： | 郭莉琴. Clean环及其扩张[J]. 天水师范学院学报, 2006, 26(5): 30-31 |
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| 作者姓名： | 郭莉琴 |
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| 作者单位： | 天水师范学院,数理与信息科学学院,甘肃,天水,741001 |
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| 摘 要： | 讨论了clean环的几个重要性质,证明了R是clean环当且仅当R上的可数(有限或列有限)的上三角矩阵环是clean环,也当且仅当R上的可数(有限或行有限)的下三角矩阵环是clean环,在一定条件下证明了clean环是Morita不变量。
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| 关 键 词： | clean环 Von Neumann正则环 上(下)三角矩阵环 形式幂级数环 斜幂级数环 |
| 文章编号： | 1371-1351(2006)05-0030-02 |
| 修稿时间： | 2006-03-07 |
Clean Rings and their Extensions |
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| Guo Liqin. Clean Rings and their Extensions[J]. Journal of Tianshui Normal University, 2006, 26(5): 30-31 |
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| Authors: | Guo Liqin |
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| Abstract: | Some properties of clean rings are discussed.It is shown that R is a clean ring if and only if every countable upper triangular matrix ring(finite or column finite) is a clean ring.In addition,under certain conditions,it is proved that clean ring is Morita invariant. |
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| Keywords: | clean ring Von Neumann regular ring upper(lower) triangular matrix ring skew power series ring |
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