Generalized derivations acting on multilinear polynomials in prime rings
On right ideals and derivations in prime rings with Engel condition
Right Sided Ideals and Multilinear Polynomials with Derivation on Prime Rings
Generalized derivations in prime rings and Banach algebras
Let R be a prime ring with extended centroid C, F a generalized derivation of R and n ≥ 1, m≥ 1 fixed integers. In this paper we study the situations: 1. for all x,y ∈ I, where I is a nonzero ideal of R; 2. (F(x∘y))ⁿ=(x∘y)ⁿ for all x,y ∈ I, where I is a nonzero right ideal of R. Moreover, we also investigate the situation in semiprime rings and Banach algebras.
Generalized derivations on Lie ideals in prime rings
Let be a prime ring with its Utumi ring of quotients and extended centroid . Suppose that is a generalized derivation of and is a noncentral Lie ideal of such that for all , where is a fixed integer. Then one of the following holds:
Derivations with power central values on Lie ideals in prime rings
Let be a prime ring of char with a nonzero derivation and let be its noncentral Lie ideal. If for some fixed integers , for all , then satisfies , the standard identity in four variables.
Vanishing power values of commutators with derivations on prime rings.
Remarks on generalized derivations in prime and semiprime rings.
Vanishing power values of commutators with derivations.
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