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An Engel condition with two generalized derivations in prime rings
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In this article, the authors consider a noncommutative prime ring with extended centroid C and maximal right ring of quotients Q, and give a generalized derivation of R.Abstract:
Let R be a noncommutative prime ring with extended centroid C and maximal right ring of quotients Q. Let I be a nonzero ideal of R, and let g, h be two generalized derivations of R. Suppose that [ ...read more
Citations
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The structure of n-commuting additive maps on Lie ideals of prime rings
Cheng-Kai Liu,Yen-Fu Pu +1 more
TL;DR: In this paper, it was shown that there exists an additive map μ : L → C such that f(x ) = λ x + μ (x ) for all x ∈ L except when char R = 2 and R ⊆ M 2 (F ), the 2 × 2 matrix ring over a field F. This result naturally generalizes the classical theorem for derivations by Lanski and the recent theorem for X-generalized skew derivations.
Journal ArticleDOI
b′-Generalized skew derivations acting as a Jordan derivation on multilinear polynomials in prime rings
Ashutosh Pandey,Giovanni Scudo +1 more
TL;DR: In this article , the complete structure of skew derivations on a prime ring of characteristic not equal to 2 is studied for all π > 0, where π is a noncentral multilinear polynomial.
Journal ArticleDOI
An Engel condition with two generalized derivations on Lie ideals of prime rings
TL;DR: In this article , the authors characterize the structure of generalized derivations of formula see text and all possible forms of [formula see text] and [Formula: see text].
b-generalized skew derivations acting as 2-Jordan multiplier on multilinear polynomials in prime rings
TL;DR: In this paper , the identity of a prime ring of characteristic not equal to 2 is investigated, and two skew derivations of R satisfying the identity are presented, where φ ( ζ 1 ..., ζ n ) is a non central multilinear polynomial over C , and F , G are two b-generalized skew derivation of R.
Journal ArticleDOI
Pair of Generalized Derivation on Lie Ideals in Prime Ring
TL;DR: In this article , it was shown that there exists a generalized derivation on [Formula: see text] such that [formula see text], for all [See text] satisfies the standard identity [See Text] for all.
References
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Journal ArticleDOI
Derivations in prime rings
TL;DR: In this paper, it was shown that in a prime ring of characteristics not 2, if the iterate of two derivations is a derivation, then one of them is zero; and if d is a derived ring such that, for all elements a of the ring, ad(a)-d(a)a is central, then either the ring is commutative or d is zero.
Book
Rings with Generalized Identities
TL;DR: Preliminaries ring of quotients orthogonal completions primitive rings with GPI T-identities of prime rings and semiprime rings applications of Lie theory as mentioned in this paper.
Book
Topics In Ring Theory
TL;DR: In this article, the authors make a study of rings satisfying certain ascending chain conditions and show that the decisive and incisive results are three theorems due to Goldie, and the main part of the chapter is devoted to a presentation of these.
Journal ArticleDOI
On the distance of the composition of two derivations to the generalized derivations
TL;DR: In this article, the authors generalized Posner's theorem to arbitrary C*-algebras and extended it to C *-algebraic linear operators on a Banach space (see, e.g., [1], [2], [3] and [4] ).
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