| Semicommutative Subrings of Matrix Rings |
| Received:September 13, 2004 |
| Key Words:
semicommutative ring Armendariz ring reduced ring.
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| Fund Project:the National Natural Science Foundation of China (10171082), TRAPOYT, and NWNU-KJCXGC212 |
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| Abstract: |
| A ring $R$ is called semicommutative if for every $a\in R$, $r_R(a)$ is an ideal of $R$. It is well-known that the $n$ by $n$ upper triangular matrix ring is not semicommutative for any ring $R$ with identity when $n\geq 2$. We show that a special subring of upper triangular matrix ring over a reduced ring is semicommutative. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2006.02.011 |
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