AN EXTENSION OF RINGS AND HOCHSCHILD 2-COCYCLES

Abstract

The focus of this paper is on a ring construction H-sigma(R; R) based on a given ring R and a Hochschild 2-cocycle a. This construction is a unified generalization of the ring R[x]/(x(n+1)) and the Hochschild extension H-sigma(R, R). Here we discuss when the ring H-n(R; sigma) is reversible, symmetric, Armendariz, abelian and uniquely clean, respectively. Several known results of R[x]/(x(n+1)) and H-sigma (R, R) are extended to H-n(R; sigma), and new examples of reversible, symmetric and Armendariz rings are given.