- Hacettepe Journal of Mathematics and Statistics
- Vol: 44 Issue: 5
- Some results on σ-ideal of σ-prime ring
Some results on σ-ideal of σ-prime ring
Authors : Selin Türkmen, Neşet Aydin
Pages : 1147-1156
View : 12 | Download : 10
Publication Date : 2015-10-01
Article Type : Research
Abstract :Let R be a σ -prime ring with characteristic not 2 , Z ( R ) be the center of R, I be a nonzero σ -ideal of R, α,β : R → R be two automorphisms, d be a nonzero ( α, β ) -derivation of R and h be a nonzero derivation of R. In the present paper, it is shown that ( i ) If d ( I ) ⊂ C α,β and β commutes with σ then R is commutative. ( ii ) Let α and β commute with σ. If a ∈ I ∩ S σ ( R ) and [ d ( I ) ,a ] α,β ⊂ C α,β then a ∈ Z ( R ) . ( iii ) Let α,β and h commute with σ. If dh ( I ) ⊂ C α,β and h ( I ) ⊂ I then R is commutative.Keywords : σ-prime ring, σ-ideal, (α, β)-derivation