IDENTITIES ON ADDITIVE MAPPINGS IN SEMIPRIME RINGS.

Consider a ring R, which is semiprime and also having k-torsion freeness. If F, d : R → R are two additive maps fulfilling the algebraic identity for each x in R. Then F will be a generalized derivation having d as an associated derivation on R. On the other hand, in this article, it is also derived that f is a generalized left derivation having a linked left derivation δ on R if they satisfy the algebraic identity for each x in R and k {2, m, n, (n + m - 1)!} and at last an application on Banach algebra is presented. [ABSTRACT FROM AUTHOR]