Diophantine undecidability for some holomorphy rings of algebraic functions of characteristic 0.

DOI10.1080/00927879408825078zbMath0810.11074OpenAlexW2059160443MaRDI QIDQ4304189

Alexandra Shlapentokh

Publication date: 10 October 1994

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879408825078

zbMATH Keywords

decidabilityHilbert's tenth problemdiophantine problemzero characteristic holomorphy rings of algebraic functions

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Decidability of theories and sets of sentences (03B25) Diophantine equations (11D99)

Related Items (4)

The logic of pseudo-\(S\)-integers ⋮ Diophantine undecidability of holomorphy rings of function fields 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 unsolvability over \(p\)-adic function fields
• Extension of Hilbert's tenth problem to some algebraic number fields
• Diophantine relationships between algebraic number fields
• Hilbert's Tenth Problem for Rings of Algebraic Functions in One Variable Over Fields of Constants of Positive Characteristic
• Diophantine Sets over Some Rings of Algebraic Integers
• Diophantine relations between rings of S-integers of fields of algebraic functions in one variable over constant fields of positive characteristic

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