The diophantine problem for addition and divisibility for subrings of rational functions over finite fields
The diophantine problem for addition and divisibility for subrings of rational functions over finite fields
Author
Cerda-Romero, Leonidas Antonio
Martínez-Ranero, Carlos
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/366610.22199/issn.0717-6279-2020-03-0045
Abstract
It is shown that the positive existential theory of the structure ?S = (S?1F[t];=,F, 0, 1,+, |, f ? tf), where f ? tf is the multiplication by t map, S is non-empty a finite set of irreducible polynomials, and F is a finite field of odd characteristic, is undecidable. It is shown that the positive existential theory of the structure ?S = (S?1F[t];=,F, 0, 1,+, |, f ? tf), where f ? tf is the multiplication by t map, S is non-empty a finite set of irreducible polynomials, and F is a finite field of odd characteristic, is undecidable.