On diophantine equations over the ring of all algebraic integers

DOI10.1016/0022-314X(84)90038-6zbMath0538.12014MaRDI QIDQ793094

Peter Roquette, David C. Cantor

Publication date: 1984

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

rational functionsHasse principlelocal-global principlering of algebraic integersalgebraic closure of algebraic number fielddecision procedure for Skolem problemsdiophantine problemstrong approximation theorem

Mathematics Subject Classification ID

Decidability and field theory (12L05) Algebraic number theory: global fields (11R99) Algebraic number theory: local fields (11S99) Non-Archimedean valued fields (12J25) Model theory of fields (12L12) Diophantine equations (11D99)

Related Items

An infinite version of Arrow's theorem in the effective setting, Groupes de Picard et problèmes de Skolem. I, Groupes de Picard et problèmes de Skolem. II, Recent results in the theory of constant reductions, Module equivalences: Local to global. When primitive polynomials represent units, Rumely’s local global principle for algebraic 𝑃𝒮𝒞 fields over rings, Picardindex und ganzalgebraische Punkte. (Picard index and integral points), Genre et genre residuel des corps de fonctions valués. (Genus and residual genus of valued function fields), Prolongement de la valeur absolue de Gauss et problème de Skolem, Relative elimination of quantifiers for Henselian valued fields

Cites Work

• Complete theories
• Module equivalences: Local to global. When primitive polynomials represent units
• On an extension of the definition of transfinite diameter and some applications.
• Algebraic integral representations by arbitrary forms
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