Unique representation domains, II

Given a star operation ∗ of finite type, we call a domain R a ∗-unique representation domain (∗-URD) if each ∗-invertible ∗-ideal of R can be uniquely expressed as a ∗-product of pairwise ∗-comaximal ideals with prime radical. When ∗ is the t-operation we call the ∗-URD simply a URD. Any unique factorization domain is a URD. Generalizing and unifying results due to Zafrullah [M. Zafrullah, On unique representation domains, J. Nat. Sci. Math. 18 (1978) 19-29] and Brewer-Heinzer [J.W. Brewer, W.J. Heinzer, On decomposing ideals into products of comaximal ideals, Comm. Algebra 30 (2002) 5999-6010], we give conditions for a ∗-ideal to be a unique ∗-product of pairwise ∗-comaximal ideals with prime radical and characterize ∗-URD's. We show that the class of URD's includes rings of Krull type, the generalized Krull domains introduced by El Baghdadi and weakly Matlis domains whose t-spectrum is treed. We also study when the property of being a URD extends to some classes of overrings, such as polynomial extensions, rings of fractions and rings obtained by the D+XDS[X] construction.