Characterizing domains of finite ∗-character

For ∗ a star operation of finite type call a domain D a domain of finite ∗-character if every nonzero nonunit of D is contained in at most a finite number of maximal ∗-ideals. We prove a result that characterizes domains of finite ∗-character and outline its applications. Applications include characterization of Prüfer and Noetherian domains of finite character and of domains of finite t-character.