- Journal of Scientific Perspectives
- Vol: 2 Issue: 3
- On the Commutativity of a Prime ∗-Ring with a ∗-α-Derivation
On the Commutativity of a Prime ∗-Ring with a ∗-α-Derivation
Authors : Gülay Bosnali, Neşet Aydin, Selin Türkmen
Pages : 51-60
View : 17 | Download : 4
Publication Date : 2018-07-31
Article Type : Research
Abstract :Let R be a prime ∗-ring where ∗ be an involution of R, α be an automorphism of R, T be a nonzero left α-∗-centralizer on R and d be a nonzero ∗-α-derivation on R. The aim of this paper is to prove the commutativity of a ∗-ring R with the followings conditions: i) if T is a homomorphism (or an antihomomorphism) on R,ii) if d([x,y]) = 0 for all x,y ∈ R, iii) if [d(x),y] = [α(x),y] for all x,y ∈ R, iv) if d(x)◦y = 0 for all x,y ∈ R, v) if d(x◦y) = 0 for all x,y ∈ R.Keywords : ∗-derivation, ∗-α-derivation, left ∗-centralizer, left α-∗-centralizer