Wedderburn polynomials over division rings, I |
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Authors: | TY Lam André Leroy |
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Institution: | a Department of Mathematics, University of California, Berkeley, CA 94720, USA b Department of Mathematics, Université d'Artois, 62307 Lens Cedex, France |
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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 Kt,S,D], where S is an endomorphism of K and D is an S-derivation on K. |
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Keywords: | Primary: 16D40 16E20 16L30 secondary: 16D70 16E10 16G30 |
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