• Corpus ID: 221172698

Operators coming from ring schemes

  title={Operators coming from ring schemes},
  author={Jakub Gogolok and Piotr Kowalski},
  journal={arXiv: Logic},
We introduce the notion of a coordinate $\mathbf{k}$-algebra scheme and the corresponding notion of a $\mathcal{B}$-operator. This class of operators includes endomorphisms and derivations of the Frobenius map, and it also generalizes the operators related to $\mathcal{D}$-rings from [15]. We classify the (coordinate) $\mathbf{k}$-algebra schemes for a perfect field $\mathbf{k}$ and we also discuss the model-theoretic properties of fields with $\mathcal{B}$-operators. 
We prove some results about the model theory of fields with a derivation of the Frobenius map, especially that the model companion of this theory is axiomatizable by axioms used byWood in the case of


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  • Piotr Kowalski
  • Mathematics, Computer Science
    Journal of Symbolic Logic
  • 2005
Abstract We prove that the theory of fields with a derivation of Frobenius has the model companion which is stable and admits elimination of quantifiers up to the level of the λ-functions. Along the
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