# Operators coming from ring schemes

@article{Gogolok2020OperatorsCF, title={Operators coming from ring schemes}, author={Jakub Gogolok and Piotr Kowalski}, journal={arXiv: Logic}, year={2020} }

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.

## One Citation

MODEL THEORY OF DERIVATIONS OF THE FROBENIUS MAP REVISITED

- MathematicsThe Journal of Symbolic Logic
- 2021

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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