A Class of Maximal General Armendariz Subrings of Matrix Rings
Received:November 11, 2006  Revised:October 28, 2007
Key Word: general Armendariz ring   matrix ring   general reduced ring.
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 Author Name Affiliation WANG Wen Kang School of Computer Science and Information Engineering, Northwest University for Nationalities, Gansu 730124, China
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An associative ring with identity $R$ is called Armendariz if, whenever $(\sum_{i=0}^{m}a_{i}x^{i})$ $(\sum_{j=0}^{n}b_{j}x^{j})=0$ in $R[x]$, $a_{i}b_{j}=0$ for all $i$ and $j$. An associative ring with identity is called reduced if it has no non-zero nilpotent elements. In this paper, we define a general reduced ring (with or without identity) and a general Armendariz ring (with or without identity), and identify a class of maximal general Armendariz subrings of matrix rings over general reduced rings.