• (α, β) DERIVATIONS AND COMMUTATIVITY IN σ-PRIME RING

Abstract

Let R be a σ-prime ring with characterstic ≠ 2 and d be a nonzero (α, β) derivation of R commuting with σ. It is prove that a non-zero (α, β)- derivation d associated with be a non-zero σ–ideal I of R which commutes σ and i) if [d(x),x] = 0 " xÎI then R is commutative ii) If d²(I) =0 then d= 0. Also we prove that R must be commutative under some suitable conditions.