On a Generalization of Semicommutative Rings
Received:July 12, 2013  Revised:February 24, 2014
Key Words: semicommutative rings   GWZI rings   trivial extension.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11171291), the Natural Science Fund for Colleges and Universities of Jiangsu Province (Grant No.11KJB110019) and the Foundation of Graduate Innovation Program of Jiangsu Province (Grant No.CXZZ12-0082).
Author NameAffiliation
Cuizhen DU School of Mathematical Sciences, Huaibei Normal University, Anhui 235000, P. R. China 
Long WANG Department of Mathematics, Southeast University, Jiangsu 210096, P. R. China 
Junchao WEI School of Mathematical Sciences, Yangzhou University, Jiangsu 225002, P. R. China 
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Abstract:
      In this paper, a generalization of the class of semicommutative rings is investigated. A ring $R$ is called left GWZI if for any $a \in R$, $l(a)$ is a GW-ideal of $R$. We prove that a ring $R$ is left GWZI if and only if $S_{3}(R)$ is left GWZI if and only if $V_{n}(R)$ is left GWZI for any $n\geq2$.
Citation:
DOI:10.3770/j.issn:2095-2651.2014.03.001
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