Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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), 275-298
MSC: Primary 11U05; Secondary 14H05
DOI: https://doi.org/10.1090/S0002-9947-1992-1091233-2
MathSciNet review: 1091233
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The author builds an undecidable model of integers with certain relations and operations in the rings of $ S$-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.


References [Enhancements On Off] (What's this?)

  • [1] 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. 323-378. 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.), North-Holland, Amsterdam, 1979, pp. 131-145. 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)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 11U05, 14H05

Retrieve articles in all journals with MSC: 11U05, 14H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1091233-2
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society