In this paper, we show that for semi-prime rings of two-torsion free and 6-centrally torsion free, given a multiplicative centrally-extended derivation δ and a multiplicative centrally-extended epimorphism ϕ we can find a central ideal K and maps Δ , Φ : S / K → S / K such as Δ and Φ are multiplicative derivation and multiplicative epimorphism, respectively. [ABSTRACT FROM AUTHOR]
Our aim in this paper is to prove some properties of semi-derivations centralizing on Jordan ideals of rings with involution. Some well known results characterizing commutativity of prime rings by derivations have been generalized by using semi-derivations. Moreover, we provide examples to show that our hypotheses are not superfluous. [ABSTRACT FROM AUTHOR]
In the present paper it is shown that 3-prime left near-rings satisfying certain identities involving generalized derivations are commutative rings. Moreover, examples proving the necessity of the 3-primeness hypothesis in various theorems are given. [ABSTRACT FROM AUTHOR]
Oukhtite, Lahcen, Mamouni, Abdellah, and Beddani, Charef
Abstract
The purpose of this paper is to study derivations satisfying certain differential identities on Jordan ideals of prime rings. Some well known results characterizing commutativity of prime rings by derivations have been generalized by using Jordan ideals. Moreover, we provide examples to show that our results cannot be extended to semi-prime rings. [ABSTRACT FROM AUTHOR]