A Class of Maximal General Armendariz Subrings of Matrix Rings

Abstract:

      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.