@article{0e746a17-1bbc-44ae-b18a-a2dccba9cd7d,
author = {Dimitra Chompitaki, Manos Kamarianakis , Thanases  Pheidas},
title = {Notes on the decidability of addition and the Frobenius map for polynomials and rational functions},
journal = {Reports on Mathematical Logic},
volume = {2022},
number = {Number 57},
year = {2022},
issn = {0137-2904},
pages = {53-60},keywords = {decidability; model completeness; Frobenius map; polynomial rings; rational functions},
abstract = {Let pbe a prime number, Fp a finite field with pelements, Fan 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.},
doi = {10.4467/20842589RM.22.004.16661},
url = {https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/notes-on-the-decidability-of-addition-and-the-frobenius-map-for-polynomials-and-rational-functions}
}