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Absolute valued algebras satisfying (x,x,x2) = 0
Authors:M L El-Mallah
Institution:Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt, EG
Abstract:Let A be an absolute valued algebra satisfying the identity (x,x,x2) = 0. We give some conditions which imply that A is isomorphic to R, \mathbbC \mathbb{C} , H or D. These results enable us to show that if A is an algebra with involution then A is one of those classical algebras. We construct an example of A having dimension two and is not isomorphic to \mathbbC \mathbb{C} .
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