  In this paper, we advance an ideal-theoretic analogue of a "finite
factorization domain" (FFD), giving such a domain the moniker "finite
molecularization domain" (FMD). We characterize FMD's as those factorable
domains (termed "molecular domains" in the paper) for which every nonzero ideal
is divisible by only finitely many nonfactorable ideals (termed "molecules" in
the paper) and the monoid of nonzero ideals of the domain is unit-cancellative,
in the language of Fan, Geroldinger, Kainrath, and Tringali. We develop a
number of connections, particularly at the local level, amongst the concepts of
"FMD", "FFD", and the "finite superideal domains" (FSD's) of Hetzel and Lawson.
Characterizations of when $k[X^2, X^3]$, where $k$ is a field, and the
classical $D+M$ construction are FMD's are provided. We also demonstrate that
if $R$ is a Dedekind domain with the finite norm property, then $R[X]$ is an
FMD.
