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