Well-behaved prime t-ideals and almost Krull domains

Abstract

Call a t-ideal I of an integral domain R well-behaved if IR_S is a t-ideal in R_S for every multiplicatively closed subset S of R that is disjoint from I. We show that the set of well-behaved t-ideals has maximal elements and use the induced star operation to study the almost Krull domains (domains whose localizations are Krull) introduced by E. Pirtle.

Keywords:

• Star operation
• t-operation
• almost Krull domain
• Prüfer v-multiplication domain

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13A15
• 13F05
• 13F20
• 13G05

Additional information

Funding

The first-named author was supported by a grant from the Simons Foundation (#354565).