SEMISTAR NORMAL PAIRS AND RELATED CHARACTERIZATIONS OF P*MDS

摘要

Given an overring extension of domains D C T, we introduce the semistar-theoretic analogues of D being integrally closed in T, (D,T) being a normal pair, D C T being a residually algebraic extension and (D,T) being a residually algebraic pair. Our main result generalizes Davis' characterization of normal pairs (D, T) as (overring) extensions D C T for which each intermediate ring is D-flat, while also generalizing some cele-brated characterizations of Priifer domains and several results of Ayache-Jaballah on residually algebraic pairs. This work also involves extending the connections between the semistar-theoretic notions of primitivity and INC-pair that were given by Chang and Fontana. Applications include several characterizations of P*MDs.