Semiderivations onσ–Prime Rings

Abstract

In this paper, we derive some results on semiderivation in σ – prime rings. If (R, σ) is a σ-prime ring with involution σ and char ≠ 2, let d be a nonzero semiderivation with g of R is centralizing, then R is commutative. Further we prove that if d commutes with σ and 0 ≠ I in a σ- Ideal of R such that either [d(x), d(y)] = 0 or d(xy) = d(yx), for all x, y Î I, then R is commutative. Finally, a σ-prime ring with char ≠ 2 possessing a nonzero semiderivation under surjective conditions must be commutative.