Wedderburn polynomials over division rings, I

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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. © 2003 Elsevier B.V. All rights reserved.

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Lam, T. Y., & Leroy, A. (2004). Wedderburn polynomials over division rings, I. Journal of Pure and Applied Algebra, 186(1), 43–76. https://doi.org/10.1016/S0022-4049(03)00125-7

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