On generalized Jordan ∗-derivation in rings

On Jordan generalized k-derivations of semiprime Γ_N-Rings

Jordan derivation on trivial extension

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

On Prime Near-Rings with Generalized Derivation

LetN be a zero-symmetric left near-ring, not necessarily with amultiplicative identity element; and letZ be its multiplicative center. DefineN to be 3-prime if for all a, b ∈ N\{0}, aNb / {0}; and callN 2-torsion-free if N, has no elements of order 2. A derivation onN is an additive endomorphism D of N such that D xy xD y D x y for all x, y ∈ N. A generalized derivation f with associated deriva...

On Jordan left derivations and generalized Jordan left derivations of matrix rings

Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...

on jordan generalized k-derivations of semiprime γ_n-rings