Polynomial composites and certain types of fields extensions

DOI10.15330/CMP.15.1.150-157arXiv2011.09904OpenAlexW3158446313MaRDI QIDQ6112595

Łukasz Matysiak

Publication date: 7 August 2023

Published in: Carpathian Mathematical Publications (Search for Journal in Brave)

Abstract: In this paper I consider polynomial composites with the coefficients from $KsubsetL$. We already know many properties, but we do not know the answer to the question of whether there is a relationship between composites and field extensions. I present the characterization of some known field extensions in terms of polynomial composites. This paper contains the opening problem of characterization of ideals in polynomial composites with respect to various field extensions. I also present the full possible characterization of certain field extensions.

Full work available at URL: https://arxiv.org/abs/2011.09904

zbMATH Keywords

Galois grouppolynomialfield extensionNoetherian ringfinite field extension

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Inverse Galois theory (12F12) Field extensions (12F99)

Related Items (7)

Field composites with a bounded purely inseparable factor ⋮ Compositum of Galois extensions of hilbertian fields ⋮ [[Publication:4461673|Title not available (Why is that?)]] ⋮ [[Publication:3369805|Title not available (Why is that?)]] ⋮ Composed products and module polynomials over finite fields ⋮ On polynomial extensions of Mori domains over countable fields ⋮ Polynomial Spaces: A New Framework for Composite-to-Prime-Order Transformations

This page was built for publication: Polynomial composites and certain types of fields extensions

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6112595)