| The Non-Singularity and Regularity of $GP$-$V'$-Rings |
| Received:August 31, 2010 Revised:November 26, 2010 |
| Key Words:
$GP$-$V'$-rings quasi $ZI$-rings MELT(MERT) rings weakly regular rings generalized regular rings.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10871106; 10901002; 10971099) and the Natural Science Foundation of Anhui Provincial Education Committee (Grant No.KJ2008A026). |
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| Abstract: |
| In this paper, we introduce a non-trivial generalization of $ZI$-rings-quasi $ZI$-rings. A ring $R$ is called a quasi $ZI$-ring, if for any non-zero elements $a,b\in R$, $ab=0$ implies that there exists a positive integer $n$ such that $a^{n}\neq 0$ and $a^{n}Rb^{n}=0$. The non-singularity and regularity of quasi $ZI$, $GP$-$V'$-rings are studied. Some new characterizations of strong regular rings are obtained. These effectively extend some known results. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.06.006 |
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