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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Flat or open implies going down

Authors: David E. Dobbs and Ira J. Papick
Journal: Proc. Amer. Math. Soc. 65 (1977), 370-371
MSC: Primary 13C10
MathSciNet review: 0441948
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Abstract: Let R, T be commutative rings with identity, and $ f:R \to T$ a unital ring homomorphism. We give an elementary, unified proof of the fact that f has the going down property, if T is flat as an R-module or if the induced map $ F:{\text{Spec}}(T) \to {\text{Spec}}(R)$ is open.

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PII: S 0002-9939(1977)0441948-9
Keywords: Going down, flat, open
Article copyright: © Copyright 1977 American Mathematical Society