Generalized Differential Identities of (Semi)Prime Rings

Let R be a semiprime ring with characteristic p 0 and R F be its left Martindale quotient ring. If (Xji) is a reduced generalized differential identity for an essential ideal of R, then (Z ij e( j )) is a generalized polynomial identity for R F , where e( j ) are idempotents in the extended centroid of R determined by j . Let R be a prime ring and Q be its symmetric Martindale quotient ring. If (Xji) is a reduced generalized differential identity for a noncommutative Lie ideal of R, then (Z ij ) is a generalized polynomial identity for [R,R]. Moreover, if (Xji) is a reduced generalized differential identity, with coefficients in Q, for a large right ideal of R, then (Z ij is a generalized polynomial identity for Q.