Geodesic
EXTENSIONS OF HILBERTIAN RINGS
Glasgow mathematical journal, Tome 62 (2020) no. 1, pp. 1-11

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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. 
JARDEN, MOSHE; RAZON, AHARON. EXTENSIONS OF HILBERTIAN RINGS. Glasgow mathematical journal, Tome 62 (2020) no. 1, pp. 1-11. doi: 10.1017/S0017089518000496
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     title = {EXTENSIONS {OF} {HILBERTIAN} {RINGS}},
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     year = {2020},
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