| On $\pi$-Semicommutative Rings |
| Received:August 26, 2015 Revised:December 03, 2015 |
| Key Words:
semicommutative rings left GWZI rings $\pi$-semicommutative rings
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| Fund Project:Supported by the Natural Foundation of Shandong Province (Grant Nos.ZR2013AL013; ZR2014AL001). |
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| Abstract: |
| A ring $R$ is said to be $\pi$-semicommutative if $a,b\in R$ satisfy $ab=0$ then there exists a positive integer $n$ such that $a^nRb^n=0$. We study the properties of $\pi$-semicommutative rings and the relationship between such rings and other related rings. In particular, we answer a question on left GWZI rings negatively. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.04.004 |
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