2 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 $F:R\longrightarrow R$ be a nonzero generalized $(m,n)$-Jordan deri…