## Journal of Symbolic Logic

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

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

#### 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

**Permanent link to this document**

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

**Mathematical Reviews number (MathSciNet)**

MR1217183

**Zentralblatt MATH identifier**

0773.11076

**JSTOR**

links.jstor.org

#### Citation

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