## Journal of Symbolic Logic

### Elimination theory for addition and the Frobenius map in polynomial rings

#### Abstract

We develop an elimination theory for addition and the Frobenius map over rings of polynomials. As a consequence we show that if F is a countable, recursive and perfect field of positive characteristic p, with decidable theory, then the structure of addition, the Frobenius map x→ xp and the property ‘x∈ F', over the ring of polynomials F[T], has a decidable theory.

#### Article information

Source
J. Symbolic Logic, Volume 69, Issue 4 (2004), 1006-1026.

Dates
First available in Project Euclid: 2 December 2004

https://projecteuclid.org/euclid.jsl/1102022210

Digital Object Identifier
doi:10.2178/jsl/1102022210

Mathematical Reviews number (MathSciNet)
MR2135654

Zentralblatt MATH identifier
1093.03019

#### Citation

Pheidas, Thanases; Zahidi, Karim. Elimination theory for addition and the Frobenius map in polynomial rings. J. Symbolic Logic 69 (2004), no. 4, 1006--1026. doi:10.2178/jsl/1102022210. https://projecteuclid.org/euclid.jsl/1102022210

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