LAUSR

We give algebraic conditions for a finite commutative algebra B B over a field of positive characteristic, which are equivalent to the companionability of the theory of fields with “ B B -operators” (i.e., the operators coming from homomorphisms into tensor products with B B ). We show that, in the most interesting case of a local B B , these model companions admit quantifier elimination in the “smallest possible” language, and they are strictly stable. We also describe the forking relation there.