Hilbert’s tenth problem for rings of algebraic functions in one variable over fields of constants of positive characteristic

Shlapentokh, Alexandra

doi:10.1090/S0002-9947-1992-1091233-2

Hilbert’s tenth problem for rings of algebraic functions in one variable over fields of constants of positive characteristic
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by Alexandra Shlapentokh

Trans. Amer. Math. Soc. 333 (1992), 275-298

DOI: https://doi.org/10.1090/S0002-9947-1992-1091233-2

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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

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