Weighted Jordan homomorphisms Bresar, M. Castillo Godoy, María Luisa Weighted Jordan homomorphism Zero Jordan product pre-serving map Zero Jordan product determined ring Matrix ring Prime ring The first author was supported by the Slovenian Research Agency (ARRS) Grant P1- 0288. The second author was suported by MCIU/AEI/FEDER Grant PGC2018-093794- B-I00, Junta de Andalucía Grant FQM-185, MIU Grant FPU18/00419 and MIU Grant EST19/00466. Let A and B be unital rings. An additive map T : A → B is called a weighted Jordan homomorphism if c = T (1) is an invertible central element and cT (x2) = T (x)2 for all x ∈ A. We provide assumptions, which are in particular fulfilled when A = B = Mn(R) with n ≥ 2 and R any unital ring with 1 2 , under which every surjective additive map T : A → B with the property that T (x)T (y) + T (y)T (x) = 0 whenever xy = yx = 0 is a weighted Jordan homomorphism. Further, we show that if A is a prime ring with char(A) 6= 2, 3, 5, then a bijective additive map T : A → A is a weighted Jordan homomorphism provided that there exists an additive map S : A → A such that S(x2) = T (x)2 for all x ∈ A. 2022-05-04T11:37:31Z 2022-05-04T11:37:31Z 2021-11-30 journal article Published version: M. Brešar & M. L. C. Godoy (2022) Weighted Jordan homomorphisms, Linear and Multilinear Algebra, DOI: [10.1080/03081087.2022.2059434] http://hdl.handle.net/10481/74695 10.1080/03081087.2022.2059434 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España Taylor & Francis