| 关于半clean群环 |
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| 引用本文： | 宋贤梅,梅玉霞.关于半clean群环[J].数学研究及应用,2017,37(2):194-198. |
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| 作者姓名： | 宋贤梅 梅玉霞 |
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| 作者单位： | 安徽师范大学数学系, 安徽 芜湖 241000,安徽师范大学数学系, 安徽 芜湖 241000 |
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| 基金项目： | 国家自然科学基金(Grant No.11401009), 安徽省自然科学基金(Grant No.1408085QA01). |
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| 摘 要： | 环$R$称为是半clean的, 是指环中的每个元素都是一个单位与一个周期元的和. clean环是半clean的. 刻画半clean群环的一般情形是不容易的. 我们的目的是考虑如下问题：若$G$ 是局部有限群或者是阶是3的循环群, 群环$RG$何时是semiclean的. clean群环上的一些已有结果被推广.
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| 关 键 词： | clean 环 半clean环 群环 局部有限群 |
| 收稿时间： | 2015/12/7 0:00:00 |
| 修稿时间： | 2016/12/2 0:00:00 |
On Semiclean Group Rings |
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| Xianmei SONG and Yuxia MEI.On Semiclean Group Rings[J].Journal of Mathematical Research with Applications,2017,37(2):194-198. |
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| Authors: | Xianmei SONG and Yuxia MEI |
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| Institution: | Department of Mathematics, Anhui Normal University, Anhui 241000, P. R. China and Department of Mathematics, Anhui Normal University, Anhui 241000, P. R. China |
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| Abstract: | A ring R with unity is called semiclean, if each of its elements is the sum of a unit and a periodic. Every clean ring is semiclean. It is not easy to characterize a semiclean group ring in general. Our purpose is to consider the following question: If G is a locally finite group or a cyclic group of order 3, then when is RG semiclean? Some known results on clean group rings are generalized. |
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| Keywords: | clean ring semiclean ring group ring locally finite group |
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