| 广义半交换环的幂零结构 |
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| 引用本文： | 何萍,赵良.广义半交换环的幂零结构[J].数学研究及应用,2022,42(2):133-144. |
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| 作者姓名： | 何萍 赵良 |
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| 作者单位： | 安徽工业大学数理科学与工程学院, 安徽 马鞍山 243002 |
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| 基金项目： | 江苏省自然科学基金(Grant No.BK20181406). |
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| 摘 要： | 研究了广义半交换环的幂零结构,定义了一类新的环类,即幂零$\alpha$-半交换环.说明了$\alpha$-半交换环与半交换环, $\alpha$-半交换环和$\alpha$-刚性环等环密切相关,通过构造反例说明了幂零$\alpha$-半交换环未必是$\alpha$-半交换环.研究了幂零$\alpha$-半交换环的各种性质,推广和统一了与环的半交换性质有关的若干结论.
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| 关 键 词： | 幂零$\alpha$-半交换环 $\alpha$-刚性环 $\alpha$-半交换环 多项式环 |
| 收稿时间： | 2021/4/4 0:00:00 |
| 修稿时间： | 2021/6/27 0:00:00 |
Nilpotent Structure of Generalized Semicommutative Rings |
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| Ping HE,Liang ZHAO.Nilpotent Structure of Generalized Semicommutative Rings[J].Journal of Mathematical Research with Applications,2022,42(2):133-144. |
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| Authors: | Ping HE Liang ZHAO |
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| Institution: | School of Mathematics and Physics, Anhui University of Technology, Anhui 243032, P. R. China |
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| Abstract: | We study the nilpotent structure of generalized semicommutative rings. The new concept of nilpotent $\alpha$-semicommutative rings is defined and studied. This class of rings is closely related to many well-known concepts including semicommutative rings, $\alpha$-semicommutative rings and weak $\alpha$-rigid rings. An example is given to show that a nilpotent $\alpha$-semicommutative ring need not be $\alpha$-semicommutative. Various properties of this class of rings are investigated. Many known results related to various semicommutative properties of rings are generalized and unified. |
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| Keywords: | nilpotent $\alpha$-semicommutative rings $\alpha$-rigid rings $\alpha$-semicommutative rings polynomial rings |
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