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- Title
NOTES ON THE DECIDABILITY OF ADDITION AND THE FROBENIUS MAP FOR POLYNOMIALS AND RATIONAL FUNCTIONS.
- Authors
CHOMPITAKI, Dimitra; KAMARIANAKIS, Manos; PHEIDAS, Thanases
- Abstract
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 → xp) 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.
- Subjects
POLYNOMIAL rings; PRIME numbers; FINITE fields
- Publication
Reports on Mathematical Logic, 2022, Issue 57, p53
- ISSN
0137-2904
- Publication type
Article
- DOI
10.4467/20842589RM.22.004.16661