Let R be an associative ring. An additive mapping F: R→ R is called a generalized
derivation if there exists a derivation d: R→ R such that F (xy)= F (x) y+ xd (y) holds for all x …

In this article, we define the following: Let N 0 be the set of all nonnegative integers and
D=(di) i∈ N 0 a family of additive mappings of a∗-ring R such that d 0= id R. D is called a …

Let R be a∗− prime ring with involution∗ and F be a nonzero (α, β)− derivation associated
with a (α, β)− derivation d commuting with∗. We prove classical results of Posner and …

Let 𝑅 be an associative ring with center 𝑍. For any 𝑥, 𝑦∈ 𝑅 the symbol [𝑥, 𝑦] represents
commutator 𝑥𝑦− 𝑦𝑥. Recall that a ring 𝑅 is prime if 𝑥𝑅𝑦= 0 implies 𝑥= 0 or 𝑦= 0. An …

Let 𝑅 be an associative ring with center 𝑍. For any 𝑥, 𝑦∈ 𝑅 the symbol [𝑥, 𝑦] represents
commutator 𝑥𝑦− 𝑦𝑥. Recall that a ring 𝑅 is prime if 𝑥𝑅𝑦= 0 implies 𝑥= 0 or 𝑦= 0. An …