Open Access
2002 Hilbert's Tenth Problem for Rings of Rational Functions
Karim Zahidi
Notre Dame J. Formal Logic 43(3): 181-192 (2002). DOI: 10.1305/ndjfl/1074290716


We show that if R is a nonconstant regular (semi-)local subring of a rational function field over an algebraically closed field of characteristic zero, Hilbert's Tenth Problem for this ring R has a negative answer; that is, there is no algorithm to decide whether an arbitrary Diophantine equation over R has solutions over R or not. This result can be seen as evidence for the fact that the corresponding problem for the full rational field is also unsolvable.


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Karim Zahidi. "Hilbert's Tenth Problem for Rings of Rational Functions." Notre Dame J. Formal Logic 43 (3) 181 - 192, 2002.


Published: 2002
First available in Project Euclid: 16 January 2004

zbMATH: 1062.03019
MathSciNet: MR2034745
Digital Object Identifier: 10.1305/ndjfl/1074290716

Primary: 03B25
Secondary: 11U05 , 12L05

Keywords: diophantine problems , function fields , undecidability

Rights: Copyright © 2002 University of Notre Dame

Vol.43 • No. 3 • 2002
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