AAU-ETD :: Browsing by Author "Gizat Alemu"

Now showing 1 - 1 of 1

A Study on Ideal with Skew Derivations of Prime Rings
(Addis Ababa University, 2024-09) Gizat Alemu; Tilahun Abebaw
In this work, we apply the theory of generalized polynomial identities with automorphism and skew derivations to investigate the commutativity of a ring R satisfying certain properties on some appropriate subset of R.Let R be a prime ring and set [x,y]1=[x , y]=xy-yx for all x,y ∈ R and inductively[x,y]k=[[x,y]k-1,y] for k> 1 . We apply the theory of generalized polynomial identities with automorphism and skew derivations to obtain the following result: Let R be a prime ring and I a nonzero ideal of R. Suppose that .(𝛿 , 𝜑) is a skew derivation of R such that 𝛿([ x,y] =[x,y]n• for all x , y ∈ I , then R is commutative.