  A subset $S$ of an integral domain $R$ is called a semidomain provided that
the pairs $(S,+)$ and $(S, \cdot)$ are semigroups with identities. The study of
factorizations in integral domains was initiated by Anderson, Anderson, and
Zafrullah in 1990, and this area has been systematically investigated since
then. In this paper, we study the divisibility and arithmetic of factorizations
in the more general context of semidomains. We are specially concerned with the
ascent of the most standard divisibility and factorization properties from a
semidomain to its semidomain of (Laurent) polynomials. As in the case of
integral domains, here we prove that the properties of satisfying the ascending
chain condition on principal ideals, having bounded factorizations, and having
finite factorizations ascend in the class of semidomains. We also consider the
ascent of the property of being atomic and that of having unique factorization
(none of them ascends in general). Throughout the paper we provide several
examples aiming to shed some light upon the arithmetic of factorizations of
semidomains.
