Wedderburn Polynomials over Division Rings
نویسندگان
چکیده
A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Special cases of such polynomials include, for instance, the minimal polynomials (over the center F = Z(K)) of elements of K that are algebraic over F . In this note, we give a survey on some of our ongoing work on the structure theory of Wedderburn polynomials. Throughout the note, we work in the general setting of an Ore skew polynomial ring K[t, S,D].
منابع مشابه
X iv : 0 70 6 . 35 15 v 1 [ m at h . R A ] 2 4 Ju n 20 07 Wedderburn Polynomials over Division Rings , II
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 [LL5]. 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...
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1. Basics 2 1.1. Commutants 2 1.2. Opposite Rings 3 1.3. Units 3 1.4. Ideals 4 1.5. Modules 4 1.6. Division rings 5 1.7. Endomorphism rings 7 1.8. Monoid Rings 8 1.9. Noetherian and Artinian Rings 11 1.10. Simple rings 15 1.11. Prime ideals and prime rings 17 1.12. Notes 18 2. Wedderburn-Artin Theory 18 2.1. Semisimple modules and rings 18 2.2. Wedderburn-Artin I: Semisimplicity of Mn(D) 20 2.3...
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