Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13C10

Retrieve articles in all journals with MSC: 13C10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0441948-9
PII: S 0002-9939(1977)0441948-9
Keywords: Going down, flat, open
Article copyright: © Copyright 1977 American Mathematical Society