On centrally extended Jordan derivations and related maps in rings

2022/01/25 by Bharat Bhushan, Gurninder S. Sandhu, Bhushan, Bharat +5
Mathematics · #16N60 #16W10 #16W25 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2202.07459

openalex publication_date 2022/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a ring and Z(R) be the center of R. The aim of this paper is to define the notions of centrally extended Jordan derivations and centrally extended Jordan ∗-derivations, and to prove some results involving these mappings. Precisely, we prove that if a 2-torsion free noncommutative prime ring R admits a centrally extended Jordan derivation (resp. centrally extended Jordan ∗-derivation) δ:R→ R such that [δ(x),x]∈ Z(R)~~(resp.~~[δ(x),x^∗]∈ Z(R))~for~all~x∈ R, where '∗' is an involution on R, then R is an order in a central simple algebra of dimension at most 4 over its center.

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