Factoring skew polynomials over Hamilton's quaternion algebra and the complex numbers

JOURNAL OF ALGEBRA

卷:427

Article

Pumpluen, S.

关键词: Skew-polynomials;    Ore rings;    Factorization;    Fundamental theorem of algebra;    Roots of polynomials;    Complex numbers;    Hamilton's quaternion algebra;   

DOI  :  10.1016/j.jalgebra.2014.12.028

来源: Elsevier

【 摘 要 】

We show that all non-constant polynomials in a skew-polynomial ring H[t; sigma, delta] over Hamilton's quaternions decompose into a product of linear factors, and that all non-constant polynomials in the skew-polynomial ring C[t; sigma, delta] decompose into a product of linear and quadratic irreducible factors. Our proofs use nonassociative algebras constructed out of skew-polynomial rings as introduced by Petit. Applying results by Petit, we also characterize the real division algebras which are two-dimensional vector spaces over C with C in their left and middle nuclei. (c) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free