JP Journal of Algebra, Number Theory and Applications
Volume 13, Issue 2, Pages 121 - 130
(April 2009)
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SATURATED CHAINS OF INTEGRALLY CLOSED OVERRINGS
Jim Coykendall (U.S.A.) and David E. Dobbs (U.S.A.)
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Abstract: If R is an integrally closed domain and
?is a minimal ring extension such that T is a Pr?omain, then R is a Pr?omain. A domain R with quotient field K is the intersection of a chain of Pr?verrings if and only if R is integrally closed and there is a saturated chain
?of overrings of R going from R to K such that each ring in
?is a Pr?omain. In particular, if R is a Krull domain of Krull dimension at least 2 with only countably many height 1 prime ideals, then R is a non-Pr?omain having a saturated chain of integrally closed overrings going from R to the quotient field of R. |
Keywords and phrases: integral domain, overring, saturated chain, integrally closed, Pr?omain, Krull domain, minimal ring extension, Krull dimension. |
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