6 problems

Let $m,n\geq 1$ be fixed integers, let $R$ be a semiprime ring satisfying suitable torsion restrictions, and let $T:R\longrightarrow R$ be a generalized $(m,n)$-Jordan centralizer.…

Let $m,n\geq 1$ be fixed integers, let $R$ be a semiprime ring satisfying suitable torsion restrictions, and let $T:R\longrightarrow R$ be an $(m,n)$-Jordan centralizer. Vukman's c…

Let $m,n\geq 1$ be fixed integers, let $R$ be a semiprime ring satisfying suitable torsion restrictions, and let $F:R\longrightarrow R$ be a nonzero generalized $(m,n)$-Jordan deri…

Let $m \geq 1$ and $n \geq 1$ be fixed integers, let $R$ be a semiprime ring with suitable torsion restrictions, and let $F:R\rightarrow R$ be a generalized $(m;n)$-Jordan derivati…

Generalized Jordan triple derivation conjecture. Every generalized Jordan triple derivation on ${\mathfrak R}$ is a generalized derivation; equivalently, there is a derivation…

Jing and Lu's conjecture. Every generalized Jordan derivation on ${\mathfrak R}$ is a generalized derivation; that is, there is a derivation…