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EXTENSIONS OF HILBERTIAN RINGS

Part of: General field theory

Published online by Cambridge University Press:  05 November 2018

MOSHE JARDEN  and
AHARON RAZON
MOSHE JARDEN
Affiliation:
School of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel e-mail: [email protected]
AHARON RAZON
Affiliation:
Elta Industry, Ashdod, Israel e-mail: [email protected]
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Abstract

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

Primary: 12E30: Field arithmetic
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 1 , January 2020 , pp. 1 - 11
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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