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.

Keywords

• power-quasi-Armendariz ring, power of coefficient, quasi-Armendariz ring, Armendariz ring, polynomial ring, matrix ring

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15. Department of Mathematics Daejin University Pocheon 487-711, Korea e-mail: [e-mail] Min Jung Lee and Yang Lee Department of Mathematics Education Pusan National University Pusan 609-735, Korea e-mails: [e-mail] (Min Jung Lee) [e-mail] (Yang Lee)