Abstract. LetRbe a finite-dimensional central simpleC-algebra with involution * of the first kind, charR≠ 2 and letE*(R)be theC-subspace ofR, spanned by all projections. In this paper we prove a proposition concerning invariant submodules in prime rings with involution and then decideE*(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.