The eigenspaces of twisted polynomials over cyclic field extensions

Adam Owen; Susanne Pumplün

doi:10.2478/auom-2023-0012

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The eigenspaces of twisted polynomials over cyclic field extensions

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 31 (2023): Issue 1 (January 2023)

By: Adam Owen and Susanne Pumplün

Open Access

|Feb 2023

Abstract

Let K be a field and σ an automorphism of K of order n. Employing a nonassociative algebra, we study the eigenspace of a bounded skew polynomial f ∈ K[t; σ]. We mainly treat the case that K/F is a cyclic field extension of degree n with Galois group generated by σ.We obtain lower bounds on the dimension of the eigenspace, and compute it in special cases as a quotient algebra. Conditions under which a monic polynomial f ∈ F [t] ⊂ K[t; σ] is reducible are obtained in special cases.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2023-0012 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 221 - 240

Submitted on: Jun 17, 2022

Accepted on: Sep 20, 2022

Published on: Feb 4, 2023

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Skew polynomial ring,

reducible skew polynomials,

eigenspace,

nonassociative algebra

Related subjects:

Mathematics,

General mathematics

© 2023 Adam Owen, Susanne Pumplün, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 31 (2023): Issue 1 (January 2023)