Semicommutative Subrings of Matrix Rings
Received:September 13, 2004  
Key Word: semicommutative ring   Armendariz ring   reduced ring.  
Fund ProjectL:the National Natural Science Foundation of China (10171082), TRAPOYT, and NWNU-KJCXGC212
Author NameAffiliation
LIU Zhong-kui Department of Mathematics, Northwest Normal University, Lanzhou 730070, China 
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      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.
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