Weighted Jordan homomorphisms

2021/11/30 by Matej Brešar, Brešar, Matej, M. L. C. Godoy +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2111.15232

openalex publication_date 2021/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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=M_n(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)≠ 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.

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