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    On a generalized identity of a prime ring involving b?generalized derivations
    (Maltepe Üniversitesi, 2019) Baydar Yarbil, Nihan
    In recent years many effective results regarding semiprime rings obtained by a number of authors. The main purpose when treating an additive map is to describe the form of the map or the structure of the ring. Recently, [2] Kosan and Lee propose a new definition: Definition 1. Let d : R ? Q be an additive map and b ? Q. An additive map F : R ? Q is called a left b?generalized derivation with associated mapping d, if F(xy) = F(x)y + bxd(y) for all x, y ? R. In the light of this definition, the main results obtained by a number of authors is stated. Let R be a prime ring and L be a noncommutative Lie ideal of R, let F be a left b?generalized derivation associated with the map d. Supposing that a is a fixed element of R such that aF(x) n = 0 for all x ? L where n is a fixed positive integer, under some assumptions on the ring, the characterization of the maps is being treated.