AN EXTENSION OF RINGS AND HOCHSCHILD 2-COCYCLES

Kosan M. T., Lee T., Zhou Y.

6th China-Japan-Korea International Conference on Ring Theory, Suweon, South Korea, 27 June - 02 July 2011, pp.29-46 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • City: Suweon
  • Country: South Korea
  • Page Numbers: pp.29-46
  • Keywords: Extension of rings, Hochschild 2-cocycle, reversible ring, symmetric ring, Armendariz ring, ARMENDARIZ RINGS, REVERSIBLE RINGS, SYMMETRIC RINGS
  • Gazi University Affiliated: No

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.