## Journal of Symbolic Logic

### Diophantine Relations between Rings of $S$-Integers of Fields of Algebraic Functions in One Variable Over Constant Fields of Positive Characteristic

Alexandra Shlapentokh

#### Abstract

One of the main theorems of the paper states the following. Let $R-K-M$ be finite extensions of a rational one variable function field $R$ over a finite field of constants. Let $S$ be a finite set of valuations of $K$. Then the ring of elements of $K$ having no poles outside $S$ has a Diophantine definition over its integral closure in $M$.

#### Article information

Source
J. Symbolic Logic, Volume 58, Issue 1 (1993), 158-192.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744183

Mathematical Reviews number (MathSciNet)
MR1217183

Zentralblatt MATH identifier
0773.11076

JSTOR
Shlapentokh, Alexandra. Diophantine Relations between Rings of $S$-Integers of Fields of Algebraic Functions in One Variable Over Constant Fields of Positive Characteristic. J. Symbolic Logic 58 (1993), no. 1, 158--192. https://projecteuclid.org/euclid.jsl/1183744183