  In this paper, we study zero divisors in Hurwitz series rings and Hurwitz
polynomial rings over general noncommutative rings. We first construct
Armendariz rings that are not Armendariz of the Hurwitz series type and find
various properties of (Hurwitz series) Armendariz rings. We show that for a
semiprime Armendariz of Hurwitz series type (so reduced) ring $R$ with $a.c.c.$
on annihilator ideals, $HR$ (the Hurwitz series ring with coefficients over
$R$) has finitely many minimal prime ideals, say $B_1, \ldots, B_m$ such that
$B_1 \cdot \ldots \cdot B_m = 0$ and $B_i = HA_i$ for some minimal prime ideal
$A_i$ of $R$ for all $i$, where $A_1, \ldots, A_m$ are all minimal prime ideals
of $R$. Additionally, we construct various types of (Hurwitz series) Armendariz
rings and demonstrate that the polynomial ring extension preserves the
Armendarizness of the Hurwitz series as the Armendarizness.
