Model theory of fields with free operators in positive characteristic
Published in Trans. Amer. Math. Soc., 2019
Recommended citation: Beyarslan, Ö., Hoffmann, D. M., Kamensky, M., & Kowalski, P. (2019). Model theory of fields with free operators in positive characteristic. Trans. Amer. Math. Soc., 372(8), 5991–6016. https://doi.org/10.1090/tran/7896
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 admit quantifier elimination in the "smallest possible" language and they are strictly stable. We also describe the forking relation there.