Prime rings
Symmetric Skew Reverse n-Derivations on Prime Rings and Semiprime rings
... of prime rings was introduced by Bresar and Vukman ...on prime rings and semi prime rings in connection with derivations, skew derivations, reverse derivations, skew reverse ...
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Left Generalized Derivations and Commutativity of Prime Rings
... The study of the commutativity of prime rings with derivations was initiated by E.C.Posner[12]. Hvala [8] studied generalized derivations in prime rings. Daif and Bell [6] established that if ...
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On Ideals and Commutativity of Prime Rings with Generalized Derivations
... in prime rings as well as the commutativity of prime rings that consider derivations and generalized derivations, see for example [2], [3], [5] and ...free prime ring with center Z(R) ...
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Generalized derivations in prime rings
... a prime ring R which acts as homomorphisms or anti-homomorphisms on a nonzero right ideal of R then d = 0 on ...free prime ring and I be a non zero ideal of ...a prime ring with a non-zero ideal I of ...
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ClosedLieIdeals of Prime Rings with Generalizedα−derivations
... From [5], an additivemapping𝑑 from 𝑅 into 𝑅 is called derivation if 𝑑 𝑟𝑝 = 𝑑 𝑟 𝑝 + 𝑟𝑑 𝑝 for all 𝑟, 𝑝 ∈ 𝑅. In [3], Bresar introduced definition of generalized derivation. An additive mapping 𝐹 from 𝑅 into 𝑅 is called ...
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A Characterization of Derivations in Prime Rings with Involution
... Herstein. Rings with involution, The University of Chicago Press, Chicago, ...of prime rings, Kharchenko’s theorem and appli- cation, Azumaya algebras, actions, and modules (Bloomington, IN, 1990), ...
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On derivations and commutativity in prime rings
... Fact 2 . Any derivation of R can be uniquely extended to a derivation of Q, and so any derivation of R can be defined on the whole of Q [1, Proposition 2.5.1]. Moreover, Q is a prime ring as well as R and the ...
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Skew Commuting Derivations of Noncommutative Prime Rings
... on rings help us to understand rings better and also derivations on rings can tell us about the structure of the ...on prime ring forces the ring to be commutative (Posner's second ...
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Strong commutativity preserving biderivations on prime rings
... Theorem 2.1. Let R be a 2-torsionfree prime ring. If R admits a symmetric biderivation D with trace f satisfying [D(x, x), D(y, y)] = [x, y] for all x, y ∈ R, then there exist an idempotent ε ∈ C and an element α ...
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On (?,?)-Derivations and Commutativity of Prime and Semi prime ?-rings Afrah Mohammad Ibraheem
... called prime if aΓRΓb = 0 with a, b ∈R implies a = 0 or b = 0, and R is called semi prime if aΓRΓa = 0 with a ∈R implies a = ...semi-) prime Γ-ring is an extension for the notion of a ...
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Generalized Derivations of Prime Rings
... Let R be an associative ring with center Z(R). For any x, y ∈ R, the symbol [x, y] stands for the commutator xy − yx and denote by x ◦ y the anticommutator xy + yx. Given two subsets A and B of R, [A, B] will denote the ...
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Vanishing Power Values of Commutators with Derivations on Prime Rings
... Throughout this paper, unless specifically stated, R always denotes a prime ring with center ZR and extended centroid C, Q the Martindale quotients ring. Let n be a positive integer. For given a, b ∈ R, let a, b 0 ...
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Generalized higher left centralizer of prime rings
... In this paper we present the concepts of higher left centralizer, Jourdan higher left centralizer also we introduce the concepts of generalized higher left centralizer, generalized Jordan higher left centralizer of R, as ...
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On Prime and Semiprime Rings with Additive Mappings and Derivations
... on prime rings was obtained by Mayne ...noncommutative prime (and some other) ...a prime ring R of characteristic not 2 was given and subsequently in [4] the characterization for semiprime ...
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On commutativity of prime and semiprime rings with generalized derivations
... of prime rings with generalized ...a prime ring, I a nonzero ideal of R and F a generalized derivation associated with a nonzero derivation d such that F (x ◦ y) = x ◦ y for all x, y ∈ I, then R is ...
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Vol 2, No 2 (2011)
... of prime rings and are still ...of prime rings in the form of -prime rings and proved numerous results which hold true for prime rings (see for references [7 - ...
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Orthogonal reverse derivations- semiprime gamma rings
... semi prime rings have been studied by Samman and Alyamani ...semi prime rings by using reverse ...semi prime ring initiated by Bresar and Vukman ...semi prime ring and they ...
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Left Generalized Derivations on Prime Γ-Rings
... gamma rings Bresar [2] studied on the distance of the composition of two derivations to the generalized ...on prime ring is ...on prime rings, Ozturk et al. [10] studied on derivations of ...
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On Commutativity of *-Prime Near-Rings with Derivations
... ∗-prime rings and proved the following: Let R be a ∗-prime ring having nonzero ∗-ideal I then (i) If d is a nonzero derivation on R which commutes with ∗ and [x, R]Id(x) = {0} for all x ∈ I, then R ...
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On Pseudo-valuation rings and their extensions
... all rings are associative with identity 1 6 = ...each prime ideal P of R is strongly prime (ab ∈ P , a ∈ F , b ∈ F implies that either a ∈ P or b ∈ P ...
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