V. Bavula

activity

20242026

collaborators

5 papers

math.RA2026

Explicit descriptions of the subfields $(N L)^{p i}$ and $(N L)^{p i} (N L)^{se p}$ of $N L$ and new explicit criteria for $N L = (N L)^{p i} (N L)^{se p}$

V. V. Bavula

Let $L = K (I^¸) ≃ K [x] / f (x)$ be a simple field extension in prime characteristic $p > 0$ , $L^{se p}$ and $L^{p i}$ be the maximal separable and purely inseparable subfields of $L$ , re…

math.NT2026

Analogue of the Galois Theory for arbitrary finite field extensions

V. V. Bavula

This paper is a finishing touch to the (over 200 years) {\em classical} `Galois Theory' of {\em arbitrary} finite field extensions, i.e. the goal of it is to describe intermediate…

math.NT2026

Analogue of the Galois Theory for normal fields and B-extensions (characteristic free approach)

V. V. Bavula

The aim of the paper is to introduce B-extensions which are the most symmetrical finite field extensions (a finite field extension $L / K$ is called a {\it B-extension} if the endomo…

math.NT2025

The Galois Theory (a ring theoretic approach)

V. V. Bavula

The fundamental concepts in the Galois Theory are separable, normal and Galois field extensions. These concepts are central in proofs of the Galois Theory. In the paper, we introdu…

math.RA2024

Affirmative answer to the Question of Leroy and Matczuk on injectivity of endomorphisms of semiprime left Noetherian rings with large images

V. V. Bavula

The class of semiprime left Goldie rings is a huge class of rings that contains many large subclasses of rings -- semiprime left Noetherian rings, semiprime rings with Krull dimens…

Explicit descriptions of the subfields (NL)pi and (NL)pi(NL)sep of NL and new explicit criteria for NL=(NL)pi(NL)sep

Analogue of the Galois Theory for arbitrary finite field extensions

Analogue of the Galois Theory for normal fields and B-extensions (characteristic free approach)

The Galois Theory (a ring theoretic approach)

Affirmative answer to the Question of Leroy and Matczuk on injectivity of endomorphisms of semiprime left Noetherian rings with large images

Explicit descriptions of the subfields $(N L)^{p i}$ and $(N L)^{p i} (N L)^{se p}$ of $N L$ and new explicit criteria for $N L = (N L)^{p i} (N L)^{se p}$