ABSTRACT
In this chapter we generalize the construction of Hamilton quaternions and show that, over an arbitrary field K of characteristic ≠ 2, there exist 4-dimensional central simple algebras called quaternion algebras. We also discuss the problem of identifying quaternion algebras up to algebra isomorphism. The best solution reduces the problem to deciding whether quaternion algebras are isometric when viewed as bilinear spaces with the norm form defined by the quaternion algebra norm.
