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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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