Wedderburn polynomials over division rings, I

By T. Lam, A. Leroy. 2000

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Abstract 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 properties and characterizations of Wedderburn polynomials over K , and show that these polynomials form a complete modular lattice that is dual to the lattice of full 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 .

Subfields: Algebra and Number Theory, Geometry and Topology

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