2017/12/19 by Evan Houston, Muhammad Zafrullah, Houston, Evan +1
Mathematics · #13A05 #13A15 #13F05 #13G05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A05 #msc:13A15 #msc:13F05 #msc:13G05
paper · pdf · doi:10.48550/arxiv.1712.06725
arxiv created 2017/12/19 · arxiv updated 2017/12/20
For a finite-type star operation ⋆ on a domain R, we say that R is ⋆-super potent if each maximal ⋆-ideal of R contains a finitely generated ideal I such that (1) I is contained in no other maximal ⋆-ideal of R and (2) J is ⋆-invertible for every finitely generated ideal J ⊇ I. Examples of t-super potent domains include domains each of whose maximal t-ideals is t-invertible (e.g., Krull domains). We show that if the domain R is ⋆-super potent for some finite-type star operation ⋆, then R is t-super potent, we study t-super potency in polynomial rings and pullbacks, and we prove that a domain R is a generalized Krull domain if and only if it is % t -super potent and has t-dimension one.