For a finite-type star operation on a domain , we say that is -super potent if each maximal -ideal of contains a finitely generated ideal such that (1) is contained in no other maximal -ideal of and (2) is -invertible for every finitely generated ideal . Examples of -super potent domains include domains each of whose maximal -ideals is -invertible (e.g., Krull domains). We show that if the domain is -super potent for some finite-type star operation , then is -super potent, we study -super potency in polynomial rings and pullbacks, and we prove that a domain is a generalized Krull domain if and only if it is -super potent and has -dimension one.
"$\star$-super potent domains." J. Commut. Algebra 12 (4) 489 - 507, Winter 2020. https://doi.org/10.1216/jca.2020.12.489