Let M be a von Neumann algebra and : M ! M be a homomorphism. The is called a centrally extendable homomorphism (CEH) if there is a maximal abelian subalgebra (masa) M of the commutant M0 of M and a surjective homomorphism :M!M such that (Z) = (Z) for all Z in the center of M. A derivation : M ! M is called a centrally extendable derivation (CED) if there is a masaMof M0 such that has a norm preserving extension ˜ : C(M,M) ! C(M,M) which is a -˜-derivation for some -homomorphism ˜C(M,M) ! C(M,M) as an extension of , where C(M,M) is the C-algebra generated by M[M. In this paper we give some sufficient conditions for a -homomorphism to be a CEH and prove that  is a CED if and only if  is a CEH. Thus the study of -derivations on arbitrary von Neumann algebras is reduced to the case of type I von Neumann algebras.

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