We give algebraic conditions for a finite commutative 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.
- Derivations in positive characteristic
- Model companion
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics