Abstract
Let $R$ be a prime ring and $U$ be a nonzero ideal of $R$. If $T$ is a nontrivial automorphism or derivation of $R$ such that $u{u^T} - {u^T}u$ is in the center of $R$ and ${u^T}$ is in $U$ for every $u$ in $U$, then $R$ is commutative. If $R$ does not have characteristic equal to two, then $U$ need only be a nonzero Jordan ideal.
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