Addendum to “Factoring skew polynomials over Hamilton's quaternion algebra and the complex numbers” [J. Algebra 427 (2015) 20–29]

Let D be the quaternion division algebra over a real closed field F. Then every non-constant polynomial in a skew-polynomial ring D[t;σ,δ] decomposes into a product of linear factors, and thus has a zero in D. This improves [8, Theorem 2].

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Bibliographic Details
Published in:Journal of algebra Vol. 440; pp. 639 - 641
Main Author: Pumplün, S.
Format: Journal Article
Language:English
Published: Elsevier Inc 30.07.2015
Subjects:
Factorization theorem
Ore rings
Real closed field
Roots of polynomials
Skew-polynomials
secondary
Roots of polynomials
Skew-polynomials
Factorization theorem
Real closed field
Ore rings
primary
ISSN:0021-8693, 1090-266X
Online Access:Get full text
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Summary:Let D be the quaternion division algebra over a real closed field F. Then every non-constant polynomial in a skew-polynomial ring D[t;σ,δ] decomposes into a product of linear factors, and thus has a zero in D. This improves [8, Theorem 2].
Bibliography:addendum
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2015.06.014