EXTENSIONS of HILBERTIAN RINGS

Moshe Jarden; Aharon Razon

doi:10.1017/S0017089518000496

EXTENSIONS of HILBERTIAN RINGS

Moshe Jarden
, Aharon Razon

School of Mathematical Sciences

Elta Electronics Industries Ltd.

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	1-11
Number of pages	11
Journal	Glasgow Mathematical Journal
Volume	62
Issue number	1
DOIs	https://doi.org/10.1017/S0017089518000496
State	Published - 1 Jan 2020

Keywords

Mathematics Subject Classification 12E30

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10.1017/S0017089518000496

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title = "EXTENSIONS of HILBERTIAN RINGS",

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.",

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AB - 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.

KW - Mathematics Subject Classification 12E30

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EXTENSIONS of HILBERTIAN RINGS

Abstract

Keywords

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