  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.
