A Study on Ideal with Skew Derivations of Prime Rings
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Date
2024-09
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Addis Ababa University
Abstract
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 ā 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 .(šæ , š) is a skew derivation of R such that šæ([ x,y] =[x,y]nā¢ for all x , y ā I , then R is commutative.
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Keywords
Skew Derivations, Prime Rings, Automorphism