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Questions about rings that are not necessarily commutative.
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In commutativity theorems in ring theory
Suppose that $R$ is a ring such that for any $x\in R$ there exists $1<n(x)\in \mathbb{N}$ such that $x^{n(x)}-x\in Z(R)$. Prove that $R$ is commutative or if it is not commutative, then the ideal gene …