Hilbert's Tenth Problem for rings of algebraic functions of characteristic 0

DOI10.1016/0022-314X(92)90041-MzbMath0746.03008MaRDI QIDQ1183265

Alexandra Shlapentokh

Publication date: 28 June 1992

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

zbMATH Keywords

Hilbert's Tenth ProblemDiophantine definitionsrings of algebraic functions

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Decidability of theories and sets of sentences (03B25) Global ground fields in algebraic geometry (14G25)

Related Items (6)

Diophantine undecidability for some holomorphy rings of algebraic functions of characteristic 0. ⋮ The logic of pseudo-\(S\)-integers ⋮ Diophantine undecidability of holomorphy rings of function fields of characteristic 0 ⋮ First-order definitions of rational functions and \({\mathcal S}\)-integers over holomorphy rings of algebraic functions of characteristic 0 ⋮ DIOPHANTINE DEFINABILITY OVER HOLOMORPHY RINGS OF ALGEBRAIC FUNCTION FIELDS WITH INFINITE NUMBER OF PRIMES ALLOWED AS POLES ⋮ On Dipphantine definability and decidability in some rings of algebraic functions of characteristic 0

Cites Work

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• Diophantine definitions for some polynomial rings
• Diophantine relationships between algebraic number fields
• The Diophantine Problem for Polynomial Rings and Fields of Rational Functions

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