Model theory of fields with free operators in positive characteristic

Özlem Beyarslan, Daniel Max Hoffmann, Moshe Kamensky, Piotr Kowalski

Published 2018-06-01Version 1

We give algebraic conditions about a finite algebra $B$ over a perfect field of positive characteristic, which are equivalent to the companionability of the theory of fields with "$B$-operators" (i.e. the operators coming from homomorphisms into tensor products with $B$). We show that, in the most interesting case of a local $B$, these model companions are strictly stable, and we also describe the forking relation there.