QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS

Abstract

The study of Armendariz rings was initiated by Rege and Chhawchharia, based on a result of Armendariz related to the structure of reduced rings. Armendariz rings were generalized to quasi-Armendariz rings by Hirano. We introduce the concept of power-quasi-Armendariz (simply, p.q.- Armendariz) ring as a generalization of quasi-Armendariz, applying the role of quasi-Armendariz on the powers of coefficients of zero-dividing polynomials. In the process we investigate the power-quasi-Armendariz property of several ring extensions, e.g., matrix rings and polynomial rings, which have roles in ring theory.