On some classes of integral domains with finitely many star operations of finite type

Abstract

Let $R$ be an integral domain. We investigate when $R$ has only finitely many star operations of finite type. We start by investigating some classes of integral domains with at most two star operations of finite type. Our aim is to generalize or find analogues of several characterizations of well-known classes of integral domains with at most two star operations. Next we concentrate on Mori domains with only finitely many star operations of finite type in a similar study done for Noetherian domains. We end by a section on pullbacks to enrich the literature with new and original examples and also to illustrate several results in the paper.