Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2023
Committee Chair or Co-Chairs
Rodney Keaton
Committee Members
Robert Gardner, Robert Beeler
Abstract
The quaternions are an extension of the complex numbers which were first described by Sir William Rowan Hamilton in 1843. In his description, he gave the equation of the multiplication of the imaginary component similar to that of complex numbers. Many mathematicians have studied the zeros of quaternionic polynomials. Prominent of these, Ivan Niven pioneered a root-finding algorithm in 1941, Gentili and Struppa proved the Fundamental Theorem of Algebra (FTA) for quaternions in 2007. This thesis finds the zeros of quaternionic polynomials using the Fundamental Theorem of Algebra. There are isolated zeros and spheres of zeros. In this thesis, we also find the automorphisms of the zeros of the polynomials and the automorphism group.
Document Type
Thesis - unrestricted
Recommended Citation
Ogunmefun, Olalekan, "Roots of Quaternionic Polynomials and Automorphisms of Roots" (2023). Electronic Theses and Dissertations. Paper 4186. https://dc.etsu.edu/etd/4186
Copyright
Copyright by the authors.
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons, Other Physical Sciences and Mathematics Commons