Action of multiplicative (generalized)-derivations and related maps on square closed Lie ideals in prime rings - Dhara, B. (Matematychni Studii, 2025)
Let R be a prime ring and L a nonzero square closed Lie ideal of R. Suppose F,G,HR→ Rare three multiplicative (generalized)-derivations associated with the maps δ,g, hR→ R respectively which are not necessarily additive or derivations. Assume that E,TR→ R be any two maps (not necessarily additive). Let dR→ R be a nonzero derivation of R. In the present article, following identities are studied (1) d(x)F(y)+G(y)d(x)± (E(x)y+yT(u))=0, (2) H(xy)+G(y)F(x)± (E(y)x+xT(y))=0, (3) T(xy)+G(x)y± (yx+xy)=0, (4) F(x)F(y)+T(x)y± yx=0, (5) d(x)d(y)+T(x)y+F(yx)=0, for all x,yL.