Density theorems and its applications

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.