| Popis: |
We show that all non-constant polynomials in a skew-polynomial ring H [ t ; σ , δ ] over Hamilton's quaternions decompose into a product of linear factors, and that all non-constant polynomials in the skew-polynomial ring C [ t ; σ , δ ] 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. |
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