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Going Down and Open Extensions
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1975
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