TY - JOUR
TI - Notes on the decidability of addition and the Frobenius map for polynomials and rational functions
AU - Chompitaki, Dimitra
AU - Kamarianakis, Manos
AU - Pheidas, Thanases
TI - Notes on the decidability of addition and the Frobenius map for polynomials and rational functions
AB - 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.
VL - 2022
IS - Number 57
PY - 2022
SN - 0137-2904
C1 - 2084-2589
SP - 53
EP - 60
DO - 10.4467/20842589RM.22.004.16661
UR - 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
KW - decidability
KW - model completeness
KW - Frobenius map
KW - polynomial rings
KW - rational functions