Model theory of fields with free operators in positive characteristic
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- by Özlem Beyarslan, Daniel Max Hoffmann, Moshe Kamensky and Piotr Kowalski PDF
- Trans. Amer. Math. Soc. 372 (2019), 5991-6016 Request permission
Abstract:
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.References
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Additional Information
- Özlem Beyarslan
- Affiliation: Boǧaziçi Üniversitesi, Istanbul, Turkey
- Email: ozlem.beyarslan@boun.edu.tr
- Daniel Max Hoffmann
- Affiliation: Instytut Matematyki, Uniwersytet Warszawski, Warszawa, Poland
- MR Author ID: 1090372
- Email: daniel.max.hoffmann@gmail.com
- Moshe Kamensky
- Affiliation: Department of Mathematics, Ben-Gurion University, Beer-Sheva, Israel
- MR Author ID: 817736
- Email: kamenskm@math.bgu.ac.il
- Piotr Kowalski
- Affiliation: Instytut Matematyczny, Uniwersytet Wrocławski, Wrocław, Poland
- MR Author ID: 658570
- Email: pkowa@math.uni.wroc.pl
- Received by editor(s): July 1, 2018
- Received by editor(s) in revised form: May 2, 2019
- Published electronically: July 30, 2019
- Additional Notes: The second author was supported by Narodowe Centrum Nauki grants no. 2016/21/N/ST1/01465, and no. 2015/19/B/ST1/01150.
The third author’s research was supported by the Israel Science foundation (grant no. 1382/15)
The fourth author was supported by Narodowe Centrum Nauki grants no. 2015/19/B/ST1/01150, no. 2015/19/B/ST1/01151, and no. 2018/31/B/ST1/00357. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 5991-6016
- MSC (2010): Primary 03C60; Secondary 12H05, 03C45
- DOI: https://doi.org/10.1090/tran/7896
- MathSciNet review: 4014300