The eigenspaces of twisted polynomials over cyclic field extensions

Let be a field and an automorphism of of order . Employing a nonassociative algebra, we study the eigenspace of a bounded skew polynomial ∈ ; ]. We mainly treat the case that is a cyclic field extension of degree with Galois group generated by .We obtain lower bounds on the dimension of the eigenspa...

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Published inAnalele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică Vol. 31; no. 1; pp. 221 - 240
Main Authors Owen, Adam, Pumplün, Susanne
Format Journal Article
LanguageEnglish
Published Sciendo 01.01.2023
Subjects
eigenspace
nonassociative algebra
Primary: 17A35
reducible skew polynomials
Secondary: 17A60, 17A36, 16S36
Skew polynomial ring
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Summary:Let be a field and an automorphism of of order . Employing a nonassociative algebra, we study the eigenspace of a bounded skew polynomial ∈ ; ]. We mainly treat the case that is a cyclic field extension of degree with Galois group generated by .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 ∈ [ ] ⊂ ; ] is reducible are obtained in special cases.
ISSN:1844-0835
DOI:10.2478/auom-2023-0012