摘要
An associative ring with identity R is called Armendariz if, whenever (∑^m i=0^aix^i)(∑^n j=0^bjx^j)=0 in R[x],aibj=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.
An associative ring with identity R is called Armendariz if, whenever (∑^m i=0^aix^i)(∑^n j=0^bjx^j)=0 in R[x],aibj=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.