On the Ascent of Properties Related to Unique Factorization Domains

In this article, we develop equivalent conditions for a certain class of monoidal transform to inherit either the property of being a completely integrally closed domain that satisfies the ascending chain condition on principal ideals, the property of being a Mori domain, the property of being a Krull domain, or the property of being a unique factorization domain, respectively. Such a class of monoidal transform is given in terms of an (analytically) independent set that forms a prime ideal in the base domain. Characterizations are provided illustrating the necessity of the “prime ideal” hypothesis when the base domain is a Noetherian unique factorization domain.