In this survey paper, we present an historical account on derivations,(θ, φ)-derivations,
Jordan derivations, generalized derivations, generalized (θ, φ)-derivations, generalized …

Let R be a ring. A map F: R → RF: R→ R is called a multiplicative (generalized)-derivation if
F (xy)= F (x) y+ xg (y) is fulfilled for all x, y ∈ R x, y∈ R where g: R → R g: R→ R is any map …

Let R be a prime ring with center Z (R), I a non-zero ideal of R and α: R → R α: R→ R any
mapping on R. Suppose that G and F are two generalized derivations associated with …

Let N be a prime near-ring. We show two main results on the commutativity of N:(1) If there
exist k, l∈ ℕ such that N admits a generalized derivation D satisfying either D ([x, y])= xk [x …

Let R be a ring and α, β be endomorphisms of R. An additive mapping F: R→ R is called a
generalized (α, β)-derivation on R if there exists an (α, β)-derivation d: R→ R such that F …

Let R be a ring with center Z and I a nonzero ideal of R. An additive mapping F: R→ R is
called a generalized derivation of R if there exists a derivation d: R→ R such that F (xy)= F …

Let R be an associative ring. An additive mapping H: R—> R is called a left multiplier if H
(xy)= H (x) y, holds for all x, y 6 R. In this paper, we investigate commutativity of prime rings …

Let R be a semiprime ring with center Z (R). A mapping F: R→ R (not necessarily additive) is
said to be a multiplicative (generalized)-derivation if there exists a map f: R→ R (not …

Some theorems of commutativity on semiprime rings with mappings Page 1 Some theorems
of commutativity on semiprime rings with mappings SK Tiwari ∗ Department of Mathematics …

arXiv:2107.06769v1 [math.RA] 14 Jul 2021 Page 1 arXiv:2107.06769v1 [math.RA] 14 Jul 2021
ACTION OF PRIME IDEALS ON GENERALIZED DERIVATIONS-I NADEEM UR REHMAN1 …