Abstract
Let A and B be unital rings. An additive map is called a weighted Jordan homomorphism if is an invertible central element and for all . We provide assumptions, which are in particular fulfilled when with and R any unital ring with , under which every surjective additive map with the property that whenever xy = yx = 0 is a weighted Jordan homomorphism. Further, we show that if A is a prime ring with char, then a bijective additive map is a weighted Jordan homomorphism provided that there exists an additive map such that for all .
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