Some New Class of Absolute Valued Algebras with Left Unit

Let A be an absolute valued algebra with left unit. We prove that if A contains a nonzero central element, then A is finite dimensional and is isomorphic to mathbb R, mathbb C{mathbb {R}, mathbb {C}} or new classes of four and eight–dimensional absolute valued algebras with left unit. This is more general than those results in [2] and [3].