Evan Houston, Muhammad Zafrullah. Source: Journal of Commutative Algebra, Volume 12, Number 4, 489--507.Abstract:
For a finite-type star operation [math] on a domain [math] , we say that [math] is [math] -super potent if each maximal [math] -ideal of [math] contains a finitely generated ideal [math] such that (1) [math] is contained in no other maximal [math] -ideal of [math] and (2) [math] is [math] -invertible for every finitely generated ideal [math] . Examples of [math] -super potent domains include domains each of whose maximal [math] -ideals is [math] -invertible (e.g., Krull domains). We show that if the domain [math] is [math] -super potent for some finite-type star operation [math] , then [math] is [math] -super potent, we study [math] -super potency in polynomial rings and pullbacks, and we prove that a domain [math] is a generalized Krull domain if and only if it is [math] -super potent and has [math] -dimension one.