Resumen de When a minimal overring is a going-down domain

David E. Dobbs

• Let R contained in T be a minimal ring extension of (commutative integral) domains. If R is integrally closed in T, then R is a going-down domain if and only if T is a going-down domain. The preceding assertion can be generalized to the context of weak Baer going-down rings. If R is integrally closed and T is a Prufer domain, then R is a Prufer domain. If T is integral over R and T is a going-down domain, then R is a going-down domain if and only if the extension R contained in T satisfies the going-down property. An example is given of an integral minimal overring extension R contained in T of two-dimensional domains such that T is a going-down (in fact, Prufer) domain and R is a treed domain which is not a going-down domain.