An embedding theorem for reduced Albert algebras over arbitrary fields

Extending two classical embedding theorems of Albert-Jacobson and Jacobson for Albert (= exceptional simple Jordan) algebras over fields of characteristic not two to base fields of arbitrary characteristic, we show that any element of a reduced Albert algebra can be embedded into a reduced absolutely simple subalgebra of degree 3 and dimension 9 which may be chosen to be split if the Albert algebra was split to begin with.

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