Ali–Fošner's generalized (m,n)(m,n)-Jordan derivation conjecture

Let m,n1m,n\geq 1 be fixed integers, let RR be a semiprime ring satisfying suitable torsion restrictions, and let F:RRF:R\longrightarrow R be a nonzero generalized (m,n)(m,n)-Jordan derivation. Ali–Fošner's conjecture. Then FF is a derivation whose image is contained in Z(R)Z(R). The paper states that its first main theorem gives an affirmative answer under the explicit hypotheses that m,nm,n are distinct and RR is 6mn(m+n)mn6mn(m+n)|m-n|-torsion free.

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Primary source

Driss Bennis, Basudeb Dhara and Brahim Fahid, “On Generalized (m, n)-Jordan Derivations and Centralizers of Semiprime Rings”, arXiv:1812.08209 (2018).

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