$\mathcal {Z}$-Armendariz Rings and Modules

Abstract

In this paper we introduce and study right $\mathcal {Z}$-Armendariz rings. A ring R is said to be right $\mathcal {Z}$-Armendariz if f(x)g(x) = 0 implies that ab is a right singular element of R, where f(x) and g(x) belong to R[x] and a, b are arbitrary coefficients of f(x), g(x). Then we construct some examples of right $\mathcal {Z}$-Armendariz rings by a given one. Finally, we extend this notion for modules.