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:
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
