Norm equivalences and ideals of composition algebras

We show that linear bijections between quaternion algebras over a commutative ring preserving norms and identity elements are basically the same as isomorphisms or anti-isomorphisms. We also show that one-sided ideals of octonion algebras over a commutative ring are extended from the base.

Holger Petersson < holger.petersson@fernuni-hagen.de>