Density Theorems and Its Applications

This article is a semi-review and is also methodological innature. The article discusses generalizations of theJacobson–Chevalley density theorem, on the basis of which anumber of results from linear algebra, related to centralizers oflocally algebraic linear operators are presented. Also, based onJacobson’s approach to constructing Galois theory based on thedensity theorem, a proof of Hilbert’s theorem 90 and some of itswell-known generalizations are given.