Characterizing quaternion rings over an arbitrary base

TL;DR

This paper characterizes quaternion rings over arbitrary base rings, focusing on algebras of rank 4 with involution, and relates them to even Clifford algebra constructions.

Contribution

It provides a comprehensive characterization of quaternion rings over arbitrary bases, extending classical theory to more general settings.

Findings

Quaternion rings are precisely those algebras of rank 4 with involution constructed via even Clifford algebras.

The paper generalizes the notion of quaternion algebras to arbitrary base rings.

A new characterization criterion for quaternion rings over arbitrary bases is established.

Abstract

We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra.