| Nilpotent Structure of Generalized Semicommutative Rings |
| Received:April 04, 2021 Revised:June 27, 2021 |
| Key Words:
nilpotent $\alpha$-semicommutative rings $\alpha$-rigid rings $\alpha$-semicommutative rings polynomial rings
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| Fund Project:Supported by the Natural Science Foundation of Jiangsu Province (Grant No.\,BK20181406) and the National Natural Science Foundation of China (Grant No.12161049). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.02.004 |
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