Hilbert's tenth problem for rings of algebraic functions in one variable over fields of constants of positive characteristic
Author:
Alexandra Shlapentokh
Journal:
Trans. Amer. Math. Soc. 333 (1992), 275298
MSC:
Primary 11U05; Secondary 14H05
MathSciNet review:
1091233
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Abstract: The author builds an undecidable model of integers with certain relations and operations in the rings of integers of algebraic function fields in one variable over fields of constants of positive characteristic, in order to show that Hilbert's Tenth Problem has no solution there.
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 M. Davis, Yu. Matijasevich, and J. Robinson, Positive aspects of a negative solution, Proc. Sympos. Pure Math., vol. 28, Amer. Math. Soc., Providence, R.I., 1976, pp. 323378. MR 0432534 (55:5522)
 [2]
 J. Denef, The Diophantine Problem for polynomial rings of positive characteristic, Logic Colloquium 78 (M. Boffa, D. van Dalen, K. MacAloon, eds.), NorthHolland, Amsterdam, 1979, pp. 131145. MR 567668 (81h:03090)
 [3]
 C. Chevalley, Introduction to the theory of algebraic functions of one variable, Amer. Math. Soc., Providence, R.I., 1951. MR 0042164 (13:64a)
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DOI:
http://dx.doi.org/10.1090/S00029947199210912332
PII:
S 00029947(1992)10912332
Article copyright:
© Copyright 1992
American Mathematical Society
