FOUNDATIONS OF POLYNOMIAL THEORY IN NONCOMMUTATIVE DIVISION RINGS

By Ngo Le Hong Phuc
DOI: 10.37550/tdmu.EJS/2026.01.706

Abstract

This paper develops a systematic framework for polynomials over division algebras, focusing on degree, the Euclidean algorithm, left and right divisibility, greatest common divisors, and minimal polynomials. The relations among these notions are clarified, and conditions ensuring agreement between the left and right constructions are identified. The results extend key features of the commutative theory to the noncommutative setting.

Keywords

division algebra, Euclidean algorithm, left and right GCDs, minimal polynomials,

noncommutative polynomials, quaternion algebra

Full text

View PDF

Publication Information

Publisher

Thu Dau Mot University, Viet Nam

Editor-in-Chief

Assoc. Prof. Nguyen Van Hiep
Thu Dau Mot University

Editorial Board

Assoc. Prof. Le Tuan Anh
Thu Dau Mot University

PhD. Nguyen Quoc Cuong
Thu Dau Mot University

PhD. Doan Ngoc Xuan
Thu Dau Mot University

PhD. Nguyen Khoa Truong An
Thu Dau Mot University

Assoc. Prof. Nguyen Thanh Binh
Thu Dau Mot University

PhD. Le Thi Thuy Dung
Thu Dau Mot University

PhD. Ngo Hong Diep
Thu Dau Mot University

PhD. Nguyen Duc Dat Duc
Ho Chi Minh City University of Industry and Trade

Assoc. Prof. Nguyen Van Duc
Animal Husbandry Association of Vietnam

PhD. Nguyen Thi Nhat Hang
Department of Education and Training of Binh Duong Province

PhD. Nguyen Thi Cam Le
Vietnam Aviation Academy

PhD. Trần Hạnh Minh Phương
Thu Dau Mot University

M.A. Pham Van Thinh
Thu Dau Mot University

PhD. Nguyen Thi Lien Thuong
Thu Dau Mot University

Prof. Le Quang Tri
Can Tho University

Prof. Banh Quoc Tuan
Thu Dau Mot University