About division quaternion algebras and division symbol algebras

TL;DR

This paper identifies specific classes of division quaternion algebras over the field of rational numbers with imaginary unit and division symbol algebras over cyclotomic fields, expanding understanding of algebraic structures.

Contribution

It introduces new classes of division quaternion and symbol algebras over particular fields, contributing to algebraic theory and classification.

Findings

Identified classes of division quaternion algebras over ndield

Constructed division symbol algebras over cyclotomic fields

Enhanced classification of algebraic division structures

Abstract

{\small In this paper, we find a class of division quaternion algebras over the field }$\mathbb{Q}\left( i\right) ${\small \ and a class of division symbol algebras over a cyclotomic field.}