TY - JOUR
T1 - EXTENSIONS of HILBERTIAN RINGS
AU - Jarden, Moshe
AU - Razon, Aharon
N1 - Publisher Copyright:
Copyright © Glasgow Mathematical Journal Trust 2018.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=85056090650&partnerID=8YFLogxK
U2 - 10.1017/S0017089518000496
DO - 10.1017/S0017089518000496
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AN - SCOPUS:85056090650
SN - 0017-0895
VL - 62
SP - 1
EP - 11
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
IS - 1
ER -