Model theory of fields with free operators in positive characteristic

Özlem Beyarslan; Daniel Max Hoffmann; Moshe Kamensky; Piotr Kowalski

doi:10.1090/tran/7896

Model theory of fields with free operators in positive characteristic

Özlem Beyarslan, Daniel Max Hoffmann, Moshe Kamensky, Piotr Kowalski

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Pages (from-to)	5991-6016
Number of pages	26
Journal	Transactions of the American Mathematical Society
Volume	372
Issue number	8
DOIs	https://doi.org/10.1090/tran/7896
State	Published - 15 Oct 2019

Keywords

Derivations in positive characteristic
Model companion
Operator

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/tran/7896

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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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N2 - 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.

AB - 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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KW - Operator

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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ER -

Model theory of fields with free operators in positive characteristic

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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