On k-potent Armendariz rings

Abstract

In this paper, we introduce the concept of k-potent Armendariz rings, generalizing the notion of Armendariz rings by requiring that products of coefficients of annihilating polynomials be k-potent instead of zero. We investigate the behavior of k-potent Armendariz rings under various ring constructions, such as direct product, skew polynomial extension, trivial extension and matrix rings. Furthermore, we show that if R is a reversible ring which also satisfies k-potent Armendariz property, then R is Armendariz. Lastly, it has been shown that if R is a k-potent Armendariz ring, then R is an abelian ring and McCoy ring.