Extensions of Symmetric Rings

Abstract:

      We first consider properties and basic extensions of symmetric rings. We next argue about the symmetry of some kinds of polynomial rings, and show that if $R$ is a reduced ring then $R[x]/(x^{n})$ is a symmetric ring, where $(x^{n})$ is the ideal generated by $x^{n}$ and $n$ is a positive integer. Consequently, we prove that for a right Ore ring $R$ with $Q$ its classical right quotient ring, $R$ is symmetric if and only if $Q$ is symmetric.