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arXiv · 2311.08405

On centrally-extended Jordan endomorophisms in rings

Aziza Gouda·H. Nabiel
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Abstract

The aim of this article is to introduce the concept of centrally-extended Jordan endomorphisms and proving that if $R$ is a non-commutative prime ring of characteristic not two, and $G$ is a CE- Jordan epimorphism such that $[G(x), x] \in Z(R)$ ($[G(x), x^*] \in Z(R)$) for all $x \in R$, then $R$ is an order in a central simple algebra of dimension at most $4$ over its center or there is an element $λ$ in the extended of $R$ such that $G(x) = λx$ ($G(x) = λ^* x^*$) for all $x \in R$.

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Aziza Gouda, H. Nabiel. 2023-07-14. On centrally-extended Jordan endomorophisms in rings. https://arxiv.org/abs/2311.08405

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