An embedding theorem

We show in this paper that given any reduced, cancellative, torsion-free, atomic monoid, it is possible to construct a possibly non-atomic domain with atomic factorization structure isomorphic to the given monoid. This is significant, since atomic monoids are known to have more freedom in the factorization properties they may possess than atomic domains. This construction is motivated by the paper written by Coykendall and Zafrullah (2004) [5], in which a non-atomic domain was constructed with factorization structure isomorphic to a singly-generated monoid.