TY - JOUR AU - Cerda-Romero, Leonidas Antonio AU - Martínez-Ranero, Carlos PY - 2020/06/03 Y2 - 2024/03/28 TI - The diophantine problem for addition and divisibility for subrings of rational functions over finite fields JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 39 IS - 3 SE - DO - 10.22199/issn.0717-6279-2020-03-0045 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3666 SP - 721-735 AB - <p><em>It is shown that the positive existential theory of the structure ℱS = (S−1F[t];=,F, 0, 1,+, |, f ↦ tf), where f </em><em>↦</em><em> 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</em>.</p> ER -