On Open Ring Pairs Of Commutative Rings

• Autores: R. Douglas Chatham, David E. Dobbs
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 1, 2005, págs. 65-74
• Idioma: inglés
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• Resumen

  • If T is an integral commutative extension of a ring R such that R is an open ring, R[a, b] is a going-down ring for each a, b in T and T is semiquasilocal, then each ring contained between R and T is an open ring. An example is given to show that the "semiquasilocal" hypothesis cannot be deleted. If T is a commutative ring containing a ring R such that R[a, b] is an open ring for each a, b in T, then (R, T) is an INC-pair (equivalently, a residually algebraic pair).