JP Journal of Algebra, Number Theory and Applications
Volume 8, Issue 2, Pages 259 - 269
(August 2007)
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SEMINORMAL INTEGRAL OVERRINGS OF TWO-DIMENSIONAL GOING-DOWN DOMAINS
David E. Dobbs (U. S. A.)
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Abstract: It is proved that if T is a seminormal finitely generated integraloverring of a two-dimensional going-down domain R such that the seminormalization of R is quadratically integrally closed in T, then T is a going-down domain. The ?finitely generated? condition can be replaced by supposing that
and that
has the finite fiber property. An application is given to going-down rings with nontrivial zero-divisors. |
Keywords and phrases: going-down, integral domain, seminormal ring, integrality, overring, prime ideal, Krull dimension, divided domain, finite fiber property, conductor, quadratically integrally closed, seminormalization. |
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