On a Generalization of Semicommutative Rings |
Received:July 12, 2013 Revised:February 24, 2014 |
Key Words:
semicommutative rings GWZI rings trivial extension.
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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). |
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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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