QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS

Year 2014, Volume: 15 Issue: 15, 208 - 217, 01.06.2014

Tai Keun Kwak Min Jung Lee Yang Lee

https://doi.org/10.24330/ieja.266248

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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• 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)