Decidability of addition and Frobenius map for polynomials and rational functions

• Autorzy: Chompitaki Dimitra , Kamarianakis Manos , Pheidas Thanases

Identyfikatory

DOI

10.4467/20842589RM.22.004.16661

• Języki publikacji: EN

Abstrakty

EN

Let p be a prime number, Fp a finite field with p elements, F an algebraic extension of Fp and z a variable. We consider the structure of addition and the Frobenius map (i.e., x 7→ x p ) in the polynomial rings F[z] and in fields F(z) of rational functions. We prove that any question about F[z] in the structure of addition and Frobenius map may be effectively reduced to questions about the similar structure of the field F. Furthermore, we provide an example which shows that a fact which is true for addition and the Frobenius map in the polynomial rings F[z] fails to be true in F(z). As a consequence, certain methods used to prove model completeness for polynomials do not suffice to prove model completeness for similar structures for fields of rational functions F(z), a problem that remains open even for F = Fp

Słowa kluczowe

EN

decidability; model-completeness; Frobenius map; polynomial ring; rational function

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2022
• Tom: Vol. 57
• Strony: 53--60
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Chompitaki Dimitra

• Department of Mathematics & Applied Mathematics

autor

Kamarianakis Manos

• Department of Mathematics & Applied Mathematics

autor

Pheidas Thanases

• Department of Mathematics & Applied Mathematics

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).