The diophantine problem for addition and divisibility for subrings of rational functions over finite fields

Abstract It is shown that the positive existential theory of the structure ℱS = (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...

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Autores principales:	Cerda-Romero,Leonidas, Martínez-Ranero,Carlos
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Positive-existential definability Finite field of odd characteristic
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000300721
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spelling	oai:scielo:S0716-091720200003007212020-06-17The diophantine problem for addition and divisibility for subrings of rational functions over finite fieldsCerda-Romero,LeonidasMartínez-Ranero,Carlos Positive-existential definability Finite field of odd characteristic Abstract It is shown that the positive existential theory of the structure ℱS = (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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.3 20202020-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000300721en10.22199/issn.0717-6279-2020-03-0045
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Positive-existential definability Finite field of odd characteristic
spellingShingle	Positive-existential definability Finite field of odd characteristic Cerda-Romero,Leonidas Martínez-Ranero,Carlos The diophantine problem for addition and divisibility for subrings of rational functions over finite fields
description	Abstract It is shown that the positive existential theory of the structure ℱS = (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.
author	Cerda-Romero,Leonidas Martínez-Ranero,Carlos
author_facet	Cerda-Romero,Leonidas Martínez-Ranero,Carlos
author_sort	Cerda-Romero,Leonidas
title	The diophantine problem for addition and divisibility for subrings of rational functions over finite fields
title_short	The diophantine problem for addition and divisibility for subrings of rational functions over finite fields
title_full	The diophantine problem for addition and divisibility for subrings of rational functions over finite fields
title_fullStr	The diophantine problem for addition and divisibility for subrings of rational functions over finite fields
title_full_unstemmed	The diophantine problem for addition and divisibility for subrings of rational functions over finite fields
title_sort	diophantine problem for addition and divisibility for subrings of rational functions over finite fields
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000300721
work_keys_str_mv	AT cerdaromeroleonidas thediophantineproblemforadditionanddivisibilityforsubringsofrationalfunctionsoverfinitefields AT martinezranerocarlos thediophantineproblemforadditionanddivisibilityforsubringsofrationalfunctionsoverfinitefields AT cerdaromeroleonidas diophantineproblemforadditionanddivisibilityforsubringsofrationalfunctionsoverfinitefields AT martinezranerocarlos diophantineproblemforadditionanddivisibilityforsubringsofrationalfunctionsoverfinitefields
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The diophantine problem for addition and divisibility for subrings of rational functions over finite fields

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