Abstract
A theorem on commutativity of nonassociate ring is given.
Highlights
In 1968, Johnsen, Outcalt, and Yaqub [3] have established that a nonassociative ring R with identity 1 satisfying the relation2 = x2y2 for every x and y in R, is commutative
This naturally gives rise to the following question: what additional conditions are needed to insure the commutativity of R when R is an arbitrary ring? With this motivation, Ashraf, Quadri, and Zelinsky [1] established the following result
Let R be an associative ring with unity 1 satisfying2 = yx2y for all x, y in R, R is commutative. They used very complicated combinatorial arguments. In this connection we prove the following results
Summary
This naturally gives rise to the following question: what additional conditions are needed to insure the commutativity of R when R is an arbitrary ring? Ashraf, Quadri, and Zelinsky [1] established the following result.
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