Projections and power reduction property for generalized identities of symmetric elements

Abstract

. Let R be a finite-dimensional central simple C-algebra with involution * of the first kind, char R ≠ 2 and let E *(R)be the C-subspace of R, spanned by all projections. In this paper we prove a proposition concerning invariant submodules in prime rings with involution and then decide E *(R). As a consequence we prove the power reduction property for generalized identities of symmetric elements in a 2-torsion free semiprime ring with involution.