On the Commutativity of a Prime ∗-Ring with a ∗-α-Derivation

Authors : Gülay BOSNALI, Neşet AYDIN, Selin TÜRKMEN

Pages : 51-60

View : 14 | Download : 4

Publication Date : 2018-07-31

Article Type : Research Paper

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 insert ignore into journalissuearticles values(or an antihomomorphism); on R,ii); if dinsert ignore into journalissuearticles values([x,y]); = 0 for all x,y ∈ R, iii); if [dinsert ignore into journalissuearticles values(x);,y] = [αinsert ignore into journalissuearticles values(x);,y] for all x,y ∈ R, iv); if dinsert ignore into journalissuearticles values(x);◦y = 0 for all x,y ∈ R, v); if dinsert ignore into journalissuearticles values(x◦y); = 0 for all x,y ∈ R. 
Keywords : ∗ derivation, ∗ α derivation, left ∗ centralizer, left α ∗ centralizer