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- W2950209735 abstract "We 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." @default.
- W2950209735 created "2019-06-27" @default.
- W2950209735 creator A5020820702 @default.
- W2950209735 date "2006-06-15" @default.
- W2950209735 modified "2023-09-27" @default.
- W2950209735 title "Diophantine Definability and Decidability in the Extensions of Degree 2 of Totally Real Fields" @default.
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