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Call a  t -ideal  I  of an integral domain  R well-behaved  if  IR Sis a  t -ideal in  R Sfor 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.

Well-behaved prime t -ideals and almost Krull domains