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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 R. It is well-known that the n by n upper triangular matrix ring over any ring with identity is not semicommutative when n 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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Published by Springer since January 2013