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Published in Bollettino dell'Unione Matematica Italiana
Let (𝑋,∗,0) be a d-algebra and 𝛼,𝛽 are endomorphisms on X. Motivated by some results on derivations, (𝛼,𝛽)-derivation in rings, and the generalizations of BCK and BCI-algebras, in this paper, we introduce the notion of (𝛼,𝛽)-derivations on d-algebras, construct several examples and investigate some simple and important results.
Published in European Journal of Pure and Applied Mathematics
An additive mapping F: R → R is called a generalized derivation on R if there exists a derivation d: R → R such that F(xy) = xF(y) + d(x)y holds for all x,y ∈ R. It is called a generalized (α,β)−derivation on R if there exists an (α,β)−derivation d: R → R such that the equation F(xy) = F(x)α(y)+β(x)d(y) holds for all x,y ∈ R. In the present paper, ...
Published in Journal of Scientific Research and Reports
Let R be a prime ring with char(R) ≠ 2, Z(R) the center of R and L be a nonzero square closed Lie ideal of R. An additive mapping F : R → R is called a generalized derivation on R if there exists a derivation d : R → R such that F(xy) = xF(y) + d(x)y for all x, y ∈ R. In the present paper we shall show that L ⊆ Z(R) such that R admitting a generali...