Semistar normal pairs and related characterizations of P*MDs

Autores: David E. Dobbs, Parviz Sahandi
Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 38, Nº 3, 2012, págs. 713-739
Idioma: inglés
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Resumen
- Given an overring extension of domains D inside T, we introduce the semistar-theoretic analogues of D being integrally closed in T, (D,T) being a normal pair, D inside 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 inside T for which each intermediate ring is D-flat, while also generalizing some celebrated characterizations of Prufer 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.