Wedderburn polynomials over division rings, I

A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Such a polynomial is always a product of linear factors over K, although not every product of linear polynomials is a Wedderburn. polynomial. In this paper, we establish various proper-ties and characterizations of Wedderburn polynomials over K, and show that these polynomials form a complete modular lattice that is dual to the lattice of fall algebraic subsets of K. Throughout the paper, we work in the general setting of an Ore skew polynomial ring K[t, S, D], where S is an endomorphism of K and D is an S-derivation on K. (C) 2003 Elsevier B.V. All rights reserved.