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Vietnam Journal of Mathematics 35:3(2007) 309-315  Semicommutative and Reduced Rings Yang Gang Abstract.  A ring $R$ is called semicommutative, if $ab=0$ implies $aRb=0$ for all $a,b\in R$. It is well-known that the $n$ by $n$ upper triangular matrix ring over any ring with identity is not semicommutative when $n\geq 2$. In the paper, a special semicommutative subring of upper triangular matrix ring over a reduced ring is obtained.   2000 Mathematics Subject Classification: 16U80, 16S50. Keywords: Semicommutative ring; Armendariz ring; reduced ring.

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