Operators coming from ring schemes
Abstract
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 modeltheoretic properties of fields with $\mathcal{B}$operators.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 arXiv:
 arXiv:2008.08443
 Bibcode:
 2020arXiv200808443G
 Keywords:

 Mathematics  Logic;
 Mathematics  Rings and Algebras;
 Primary 03C60;
 Secondary 12H05;
 03C45;
 14L15