Geodesic
On Going Down in Polynomial Rings
Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 177-184

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Dawson, Jeffrey; Dobbs, David E. On Going Down in Polynomial Rings. Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 177-184. doi: 10.4153/CJM-1974-017-9
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