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On Going Down in Polynomial Rings

Published online by Cambridge University Press:  20 November 2018

Jeffrey Dawson  and
David E. Dobbs
Jeffrey Dawson
Affiliation:
Rutgers University, New Brunswick, New Jersey
David E. Dobbs
Affiliation:
Rutgers University, New Brunswick, New Jersey
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Our main purpose is to enlarge upon the studies of McAdam [9; 10] on the property of going down (GD) for prime ideals in extensions of (commutative integral) domains. Unlike the investigations of McAdam and the earlier work of Krull [8] and Cohen-Seidenberg [4] on GD and the related property of going up (GU), this paper is not primarily concerned with integral extensions. Consideration of more general extensions of domains A ⊂ B is facilitated by the following basic definitions. A prime ideal P of A is unibranched in B if there exists exactly one prime ideal Q of B satisfying Q ∩ A = P.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 177 - 184
Copyright
Copyright © Canadian Mathematical Society 1974

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