  Motivated by the study of homomorphisms and cv-polynomials presented by
Rimmer \cite{Rimmer1978} in the case of Ore extensions of automorphism type,
Ferrero and Kishimoto \cite{FerreroKishimoto1980} and Kikumasa
\cite{Kikumasa1990} in the setting of these extensions of derivation type, and
Lam and Leroy \cite{LamLeroy1992} in the context of Ore extensions of mixed
type over division rings, in this paper we investigate these both notions for
iterations of these extensions. We show that the iteration of some of the
results presented in those papers is non-trivial, and illustrate our treatment
with several noncommutative algebras.
