Classification of the finite dimensional absolute valued algebras having a non-zero central idempotent or a one-sided unity

摘要

An absolute valued algebra is a non-zero real algebra that is equipped with a multiplicative norm. We classify all finite dimensional absolute valued algebras having a non-zero central idempotent or a one-sided unity, up to algebra isomorphism. This completes earlier results of Ramírez álvarez and Rochdi which, in our self-contained presentation, are recovered from the wider context of composition k-algebras with an LR-bijective idempotent.