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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 [LL 5 ]. 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.dim C ker λ f,a = dim C ker λ h,a + dim C (Im λ h,a ∩ ker λ g,a ). But this is exactly what is given by Lemma 3.3.

A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Special cases of such polynomials include, for instance, the minimal polynomials (over the center F = Z(K)) of elements of K that are algebraic over F . In this note, we give a survey on some of our ongoing work on the structure theory of Wedderburn polynomials. Throughout the note, we work in the general setting of an Ore skew polynomial ring K[t, S, D].