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Let 푅 be a prime ring and 퐿 a non-central Lie ideal of 푅. In this paper, we aim to classify the generalized derivations of 푅 satisfying some algebraic identities with power values on 퐿. Moreover, the same identities are studied locally on a two nonvoid open subsets of a prime Banach algebra. [ABSTRACT FROM AUTHOR]

In this paper, we show that some additive mappings of a Banach algebra are derivations. Moreover, we exhibit some commutativity criteria for a prime Banach algebra admitting a derivation satisfying certain algebraic identities. [ABSTRACT FROM AUTHOR]

In this paper we consider a more general class of centralizers called I-centralizers. More precisely, given a prime ideal P of an arbitrary ring R we establish a connection between certain algebraic identities involving a pair of P-left centralizers and the structure of the factor ring R/P. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the commutativity of a Banach algebra provided with a continuous derivation satisfying algebraic identities involving nonvoid open subsets of . Furthermore, we provide examples to show that various restrictions in the hypothesis of our theorems are not superfluous. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study derivations and generalized derivations in prime rings satisfying certain differential identities. Some wellknown results characterizing commutativity of prime rings have been generalized. Moreover, we provide examples to show that the assumed restrictions cannot be relaxed. [ABSTRACT FROM AUTHOR]

The main goal of the present paper is to study some results concerning generalized derivations of prime rings with involution. Moreover, we provide examples to show that the assumed restriction cannot be relaxed. [ABSTRACT FROM AUTHOR]

In this article we investigate some commutativity criteria for a ring with involution (R , ∗ {(R,\ast}) in which generalized derivations satisfy certain algebraic identities. Moreover, we provide examples to show that the assumed restriction cannot be relaxed. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to scrutinize the deportment of generalized derivations of R satisfying some functional * {*} -identities involving the center of the factor ring R / P {R/P} where P is a prime ideal of the ring R. Moreover, we suggest to give generalization of some well known results. [ABSTRACT FROM AUTHOR]

In this article we investigate some properties of permuting n-derivations acting on a prime ideal. More precisely, let n ≤ 2 be a fixed positive integer, P be a prime ideal of a ring R such that R/P is (n+1)!-torsion free. If there exists a permuting n-derivation Δ: Rn → R such that the trace δ of Δ satisfies ... for all x ∈ R, then Δ(Rn) ⊆ P or R/P is commutative. [ABSTRACT FROM AUTHOR]