Nilpotent Structure of Generalized Semicommutative Rings
Received:April 04, 2021  Revised:June 27, 2021
Key Word: nilpotent $\alpha$-semicommutative rings   $\alpha$-rigid rings   $\alpha$-semicommutative rings   polynomial rings  
Fund ProjectL:Supported by the Natural Science Foundation of Jiangsu Province (Grant No.\,BK20181406) and the National Natural Science Foundation of China (Grant No.12161049).
Author NameAffiliation
Ping HE School of Mathematics and Physics, Anhui University of Technology, Anhui 243032, P. R. China 
Liang ZHAO 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.
Citation:
DOI:10.3770/j.issn:2095-2651.2022.02.004
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