A Note on Quaternions over Commutative Rings
arXiv:2606.23376
summary
The paper defines quaternion algebras over commutative unital rings, extends several classical properties to this setting, and investigates the structure of their unit groups, with a focus on halidon rings.
Abstract
The ring of quaternions is defined over the field of real numbers. This article extends that framework by defining quaternions over a class of commutative unital rings and generalising several of their properties. It also studies the properties of the unit group of quaternions over commutative rings with special attention to halidon rings.
16 pages
Topics & keywords
#quaternions#commutative rings#unit groups#halidon rings#ring extensionsquaternion algebracommutative unital ringunit grouphalidon ringring-theoretic properties