SYMMETRIC GENERALIZED REVERSE (α, 1)-BIDERIVATIONS IN RINGS

Abstract

Let R be a ring and α be an endomorphism of R. Then, we introduce the notions of generalized reverse (α, 1)-derivation and that of symmetric generalized reverse (α, 1)-biderivation. It is shown that if a semiprime ring admits a generalized reverse (α, 1)-derivation with an associated reverse (α, 1)-derivation d, then d maps R into Z(R) and also that if a non-commutative prime ring admits a generalized reverse (α, 1)-derivation F with an associated reverse (α, 1)-derivation d, then F is reverse left α-multiplier on R. Analogous results have been proved for a symmetric generalized reverse (α, 1)-biderivation.