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EXTENSIONS OF HILBERTIAN RINGS

Published online by Cambridge University Press:  05 November 2018

MOSHE JARDEN
Affiliation:
School of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel e-mail: jarden@post.tau.ac.il
AHARON RAZON
Affiliation:
Elta Industry, Ashdod, Israel e-mail: razona@elta.co.il
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Abstract

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We generalize known results about Hilbertian fields to Hilbertian rings. For example, let R be a Hilbertian ring (e.g. R is the ring of integers of a number field) with quotient field K and let A be an abelian variety over K. Then, for every extension M of K in K(Ator(Ksep)), the integral closure RM of R in M is Hilbertian.

MSC classification

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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