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arXiv · 0706.3515

Wedderburn polynomials over division rings, II

T. Y. Lam·A. Leroy·A. Ozturk
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Abstract

A polynomial $f(t)$ in an Ore extension $K[t;S,D]$ over a division ring $K$ is a Wedderburn polynomial if $f(t)$ is monic and is the minimal polynomial of an algebraic subset of $K$. These polynomials have been studied in "Wedderburn polynomials over division rings,I (Journal of Pure and Applied Algebra, Vol. 186, (2004), 43-76). In this paper, we continue this study and give some applications to triangulation, diagonalization and eigenvalues of matrices over a division ring in the general setting of $(S,D)$-pseudo-linear transformations. In the last section we introduce and study the notion of $G$-algebraic sets which, in particular, permits generalization of Wedderburn's theorem relative to factorization of central polynomials.

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T. Y. Lam, A. Leroy, A. Ozturk. 2007-06-24. Wedderburn polynomials over division rings, II. https://arxiv.org/abs/0706.3515

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