Algebraic Sets and Their Minimal Polynomials in a Division Ring, a General Setting

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Tayyebi, Saeed | 2016

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49096 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi-Hezavehi, Mohammad
Abstract:
A Weddernurn polynomial over a division ring K, is the minimal polynomial of an algebraic subset of K. Such a polynomial, always is a product of linear factors over K, but not all such products are Wedderburn polynomials, even if these linear factors are distinct. In this thesis, we give some properties and characterizatios of Wedderburn polynomials over the division ring K, which relates deeply to algebraic subsets of K. We work in the general setting of Ore skew polynomials with an indeterminate t over K, corresponding to S,D, where S is an endomorphism of K and D is an S-derivation over K. Also we give a survey of the structure of the skew polynomial ring K[t; S; D] and its relation with Wedderburn polynomials. Also we introduce some applications of this theory, for example in Coding theory and Control theory
Keywords:
Conjugacy Class ; Skew Polynomial Ring ; Division Rings ; Algebraic Set ; Wedderburn Polynomial