On*-bimultipliers, Generalized*-biderivations and Related Mappings

Abstract

In this paper we dene the notions of left -bimultiplier, -bimultiplier and generalized -biderivation, and to prove that if a semiprime -ring admits a left - bimultiplier M, then M maps R R into Z(R). In Section 3, we discuss the applications of theory of -bimultipliers. Further, it was shown that if a semiprime -ring R admits a symmetric generalized -biderivation G : R R ! R with an associated nonzero symmet- ric -biderivation B : R R ! R, then G maps R R into Z(R). As an application, we establish corresponding results in the setting of C -algebra.