| On Skew McCoy Rings |
| Received:January 18, 2009 Revised:January 19, 2010 |
| Key Words:
McCoy ring skew McCoy ring skew polynomial ring rigid ring skew Armendariz ring upper triangular matrix ring.
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| Fund Project:Supportd by the Natural Science Foundation of Gansu Province (Grant No.3ZS061-A25-015) and the Scientific Research Fund of Gansu Provincial Education Department (Grant No.06021-21). |
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| Abstract: |
| For a ring endomorphism $\alpha$, we introduce $\alpha$-skew McCoy rings which are generalizations of $\alpha$-rigid rings and McCoy rings, and investigate their properties. We show that if $\alpha^t=I_R$ for some positive integer $t$ and $R$ is an $\alpha$-skew McCoy ring, then the skew polynomial ring $R[x;\alpha]$ is $\alpha$-skew McCoy. We also prove that if $\alpha(1)=1$ and $R$ is $\alpha$-rigid, then $R[x;\alpha]/\langle x^2\rangle$ is $\bar{\alpha}$-skew McCoy. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.02.016 |
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