Research Information System
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, vol.56, no.1, pp.367-374, 2025 (SCI-Expanded, Scopus)
Let f : R -> R be an additive mapping and g be a function of R. If f (xy)= f (x) y+g (x) f (y)= f (x) g (y)+x f (y) and f g (x)=g f (x) for all x, y is an element of R then f is called a semi-derivation associated with g. Let R be a prime ring with characteristic different from two and lambda, mu, sigma, tau automorphisms of R. Let b be a nonzero element of R and I, J, U be nonzero ideals of R such that g(I) not equal 0. If one of the following conditions holds then R is commutative: f (I) subset of C-lambda,C-mu (J), bf (R) subset of C-lambda mu (R), f [I, J](lambda mu) = 0, [f (I), J]sigma, tau subset of C-lambda,C-mu) (U), [f (x),x](1,mu) = 0 or [f (x), g(x)](lambda,1) = 0, for all x epsilon I, [f (I), f (R)](lambda,mu) = 0. Moreover, we proved that [f (I),a](sigma, t) = 0 if and only if f [I,a](sigma, tau) = 0.