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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Model theory of fields with free operators in positive characteristic


Authors: Özlem Beyarslan, Daniel Max Hoffmann, Moshe Kamensky and Piotr Kowalski
Journal: Trans. Amer. Math. Soc. 372 (2019), 5991-6016
MSC (2010): Primary 03C60; Secondary 12H05, 03C45
DOI: https://doi.org/10.1090/tran/7896
Published electronically: July 30, 2019
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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.


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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
Email: daniel.max.hoffmann@gmail.com

Moshe Kamensky
Affiliation: Department of Mathematics, Ben-Gurion University, Beer-Sheva, Israel
Email: kamenskm@math.bgu.ac.il

Piotr Kowalski
Affiliation: Instytut Matematyczny, Uniwersytet Wrocławski, Wrocław, Poland
Email: pkowa@math.uni.wroc.pl

DOI: https://doi.org/10.1090/tran/7896
Keywords: Derivations in positive characteristic, operator, model companion
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.
Article copyright: © Copyright 2019 American Mathematical Society