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2005 | 185 | 2 | 171-194
Tytuł artykułu

Extensions of Büchi's problem: Questions of decidability for addition and kth powers

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EN
Abstrakty
EN
We generalize a question of Büchi: Let R be an integral domain, C a subring and k ≥ 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the kth powers of the unknowns, with coefficients in C?
We state a number-theoretical problem, depending on k, a positive answer to which would imply a negative answer to the question for R = C = ℤ.
We reduce a negative answer for k = 2 and for R = F(t), the field of rational functions over a field of zero characteristic, to the undecidability of the ring theory of F(t).
We address a similar question where we allow, along with the equations, also conditions of the form "x is a constant" and "x takes the value 0 at t = 0", for k = 3 and for function fields R = F(t) of zero characteristic, with C = ℤ[t]. We prove that a negative answer to this question would follow from a negative answer for a ring between ℤ and the extension of ℤ by a primitive cube root of 1.
Słowa kluczowe
Rocznik
Tom
185
Numer
2
Strony
171-194
Opis fizyczny
Daty
wydano
2005
Twórcy
  • Department of Mathematics, University of Crete, 71 409 Heraklion, Crete, Greece
  • Departamento de Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160C, Concepción, Chile
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-2-4
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