Derivations and generalized derivations
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The present paper deals with the commutativity of an associative ring R and a unital Banach Algebra A via derivations. Precisely, the study of multiplicative (generalized)-derivations F and G of semiprime (prime) ring R satisfying the... more
In this paper, it is defined that left *-α-derivation, generalized left *-α-derivation and *-α-derivation, generalized *-α-derivation of a *-ring where α is a homomorphism. The results which proved for generalized left *-derivation of R... more
This paper abstracts some results of M. Bresar and J. Vukman [1] on the orthogonal derivations of semiprime rings to (σ, τ)-derivations and generalized (σ, τ)-derivations.
In this paper, we define a set including of all fa with a ∈ R generalized derivations of R and is denoted by f R. It is proved that (i) the mapping g : L (R) → f R given by g (a) = f −a for all a ∈ R is a Lie epimorphism with kernel Nσ,τ... more
Let R be a -prime ring with characteristic not 2; Z(R) be the center of R; I be a nonzero -ideal of R; ; : R ! R be two automorphisms, d be a nonzero ( ; )-derivation of R and h be a nonzero derivation of R: In the present paper, it... more
Siberian Mathematical Journal, Vol. 48, No. 6, pp. 979983, 2007 Original Russian Text Copyright c 2007 Gölbasi ¨O. and Aydin N. ... ORTHOGONAL GENERALIZED (σ, τ)-DERIVATIONS OF SEMIPRIME RINGS ... Abstract: This paper abstracts some... more
Assume (1-5) : 1 Y = f(X) 2 Y = alpha + beta X 3 Y = alpha + beta X + u 4 Y = f(X,u) 5 Y = alpha + beta X subi + u subi i=1,2,...,n E(u subi) = 0 for all I E(u subi u subj) = { 0, sigma subu^2 } for i not equal j ; i,j =1,2, …,n for i... more
Let R be a σ−prime ring. An additive mapping F : R → R is called a generalized (α, α) − derivation, if there exists a mapping g : R → R such that F (xy) = F (x)α(y) + α (x) g(y) for all x, y ∈ R. In this paper, some results about... more
Let R be a prime ring with characteristic not two. U a (σ, τ)-left Lie ideal of R and d : R → R a non-zero derivation. The purpose of this paper is to invesitigate identities satisfied on prime rings. We prove the following results: (1)... more