Geodesic
Going Down and Open Extensions
Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 111-114

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

We call an extension of commutative rings, R ⊂ T, open if the spec mapping from spec (T) to spec (R), which sends the prime Q of T to Q ∩ R, is an open mapping. It is easy to show, as for example in [1], that if R ⊂ T is open then it satisfies going down. In general, the converse is false, as is shown by Z ⊂ (2z) with Z the integers. To the best of this author's knowledge, it is an open question whether for an integral extension, going down and open are equivalent. 
McAdam, Stephen. Going Down and Open Extensions. Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 111-114. doi: 10.4153/CJM-1975-013-5
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[1] 1. Ferrand, D., Morphisms Entiers Universellement Overt (Manuscript). Google Scholar

[2] 2. Kaplansky, I., Commutative rings (Allyn and Bacon, Boston, 1970). Google Scholar

[3] 3. Matsumura, H., Commutative algebra (Benjamin, New York, 1970). Google Scholar

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