Density theorems and its applications
https://doi.org/10.26907/2949-3919.2023.4.3-34
Abstract
This article is semi-review and is also methodological in nature. The article discusses generalizations of the Jacobson-Chevalley density theorem, on the basis of which a number of results from linear algebra are presented, related to centralizers of locally algebraic linear operators. Also, based on Jacobson’s approach to constructing Galois theory based on the density theorem, a proof of Hilbert’s theorem 90 and some of its well-known generalizations are given.
Supporting agencies: The work is supported by the Russian Science Foundation (grant no. 22-21-00267) and performed under the development program of Volga Region Mathematical Center (agreement no. 075-02-2023-944).
About the Author
A. N. Abyzov
Kazan Federal University
Russian Federation
Russian Federation
Adel Nailevich Abyzov
18 Kremlyovskaya str., Kazan 420008, Russia
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Review
For citations:
Abyzov A.N. Density theorems and its applications. Mathematics and Theoretical Computer Science. 2023;1(4):3-34. (In Russ.) https://doi.org/10.26907/2949-3919.2023.4.3-34
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