Additivity of elementary maps on alternative rings

Abstract

Let \(\mathfrak{R}\) and \(\mathfrak{R}'\) be alternative rings. In this article we investigate the additivity of surjective elementary maps of \({\mathfrak{R}\times \mathfrak{R}'}\). As a main theorem, we prove that if \(\mathfrak{R}\) contains a non-trivial idempotent satisfying some conditions, these maps are additive.