Integral domains in which each t-ideal is divisorial (Q1121945)

The authors define the notion of a TV-domain as a domain D such that each t-ideal of D is a v-ideal. The class of TV-domains includes the class of Mori domains and hence it includes Noetherian and Krull domains. The authors give some characterizations of TV-domains which have some additional properties. For example, they prove that D is a completely integrally closed TV-domain if and only if it is a Krull domain. Further, they prove that a TV-domain D is a v-domain (i.e. every nonzero finitely generated ideal of D is v-invertible) iff it is a Prüfer v- multiplication domain (PVMD), i.e. \(D_ M\) is a valuation domain for each maximal t-ideal M of D. The authors give some generalizations of results by \textit{W. Heinzer} [Mathematika 15, 164-170 (1968; Zbl 0169.054)], who studies domains all of whose nonzero ideals are v-ideals. Among these results they prove that every t-ideal of a TV-domain is contained in only finitely many maximal t-ideals. - Finally, they present some counterexamples and pose some questions.