- 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.