On maps preserving zero Jordan products. (English) Zbl 1109.16030
Using the theory of functional identities, the authors prove that if \(R\) is a ring containing 1/2, \(A=M_n(R)\) with \(n\geq 4\), and \(\theta\colon A\to A\) is additive, surjective, and satisfies \(\theta(x)\theta(y)+\theta(y)\theta(x)=0\) whenever \(x,y\in A\) with \(xy+yx=0\), then \(\theta=\lambda\varphi\) for \(\lambda=\theta(1)\) central in \(A\), and \(\varphi\colon A\to A\) a Jordan homomorphism.
Reviewer: Charles Lanski (Los Angeles)
MSC:
16W20 | Automorphisms and endomorphisms |
16W10 | Rings with involution; Lie, Jordan and other nonassociative structures |
16S50 | Endomorphism rings; matrix rings |
References:
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