Thursday, 22 August 2013

Center of Ring and commutativity

Center of Ring and commutativity

If $x^2-x$ is in $C(R)$ for all $x \in R$, prove that $R$ is commutative.
$C(R)$ is the center of the ring $\{x \in R \,|\, xa =xa,\, \forall a \in
R\}$

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