- An absolute valued algebra is a nonzero real algebra that is equipped with a multiplicative norm ||ab|| = ||a|| ||b||. We classify, by an algebraic method, all fourdimensional absolute valued algebras containing a nonzero central element and commutative sub-algebra of dimension two. Moreover, we give some conditions implying that these new algebras having sub-algebras of dimension two.

Keywords : Absolute Valued Algebra; Pre-Hilbert Algebra; Commutative Algebra; Central Element.