INTEGRAL DOMAINS WITH FINITELY MANY STAR OPERATIONS OF FINITE TYPE

Let D be an integral domain and SF (D) be the set of star operations of finite type on D. We show that if |SF (D)| < infinity, then every maximal ideal of D is a t-ideal. We give an example of integrally closed quasi-local domains D in which the maximal ideal is divisorial (so a t-ideal) but | SF (D)| = infinity. We also study the integrally closed domains D with |SF (D)| <= 2.