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Commutativity of Rings Satisfying a Polynomial Identity
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We prove the following
Theorem. If a ring with identity element 1 satisfies xk[nn,y] = [x,ym]y', for all x,y∈R where n>1 and m are fixed relatively prime positive integers and k,1 are any non-negative integers then R is commutative.
Theorem. If a ring with identity element 1 satisfies xk[nn,y] = [x,ym]y', for all x,y∈R where n>1 and m are fixed relatively prime positive integers and k,1 are any non-negative integers then R is commutative.
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