This is joint work with Özlem Beyarslan, Daniel Hoffmann and Moshe Kamensky, which is available here: https://arxiv.org/abs/1806.00464 . I will describe the set-up (introduced by Moosa and Scanlon) of "B-operators" on rings. This set-up includes derivations, Hasse-Schmidt derivations and endomorphisms. In the paper, we give algebraic conditions about a finite algebra B over a 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 admit quantifier elimination in the "smallest possible" language and they are strictly stable. We also describe the forking relation there.