Abstract
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.
Publisher
Canadian Mathematical Society
Cited by
8 articles.
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