Diophantine Definability and Decidability in the Extensions of Degree 2 of Totally Real Fields

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dc.creatorShlapentokh, Alexandra
dc.date2006-06-15
dc.date.accessioned2026-07-07T07:17:19Z
dc.date.available2026-07-07T07:17:19Z
dc.descriptionWe investigate Diophantine definability and decidability over some subrings of algebraic numbers contained in quadratic extensions of totally real algebraic extensions of $\mathbb Q$. Among other results we prove the following. The big subring definability and undecidability results previously shown by the author to hold over totally complex extensions of degree 2 of totally real number fields, are shown to hold for {\it all} extensions of degree 2 of totally real number fields. The definability and undecidability results for integral closures of ``small'' and ``big'' subrings of number fields in the infinite algebraic extensions of $\mathbb Q$, previously shown by the author to hold for totally real fields, are extended to a large class of extensions of degree 2 of totally real fields. This class includes infinite cyclotomics and abelian extensions with finitely many ramified rational primes.
dc.identifierhttps://arxiv.org/abs/math/0606368
dc.identifierhttp://arxiv.org/abs/math/0606368
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113901
dc.subjectNumber Theory
dc.subjectLogic
dc.subject11U05; 03D35
dc.titleDiophantine Definability and Decidability in the Extensions of Degree 2 of Totally Real Fields
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