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MAPS ACTING ON SOME ZERO PRODUCTS
Let $R$ be a prime ring with nontrivial idempotents. Assume $\ast$ is an involution of $R$. In this note we characterize the additive map $\delta \colon R \to R$ such that $\delta(x) y^\ast + x \delta(y)^\ast = 0$ whenever $xy^\ast = 0$ and $\phi \colon R \to R$ such that …