scholarly journals Generalization of generalized derivations acting as homomorphisms or anti-homomorphisms with central values on Lie ideals in prime rings

2015 ◽  
Vol 16 (2) ◽  
pp. 769-779 ◽  
Author(s):  
Nadeem ur Rehman ◽  
Basudeb Dhara ◽  
Mohd Arif Raza
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Central Values

Higher-order commutators with power central values on rings and algebras involving generalized derivations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Shakir Ali ◽  
Husain Alhazmi ◽  
Abdul Nadim Khan ◽  
Mohd Arif Raza
Keyword(s):  
Quotient Ring ◽  
Generalized Derivation ◽  
Higher Order ◽  
Generalized Derivations ◽  
Prime Rings ◽  
Left Multiplication ◽  
Central Values ◽  
Power Central ◽  
Rings And Algebras

AbstractLet {\mathfrak{R}} be a ring with center {Z(\mathfrak{R})}. In this paper, we study the higher-order commutators with power central values on rings and algebras involving generalized derivations. Motivated by [A. Alahmadi, S. Ali, A. N. Khan and M. Salahuddin Khan, A characterization of generalized derivations on prime rings, Comm. Algebra 44 2016, 8, 3201–3210], we characterize generalized derivations and related maps that satisfy certain differential identities on prime rings. Precisely, we prove that if a prime ring of characteristic different from two admitting generalized derivation {\mathfrak{F}} such that {([\mathfrak{F}(s^{m})s^{n}+s^{n}\mathfrak{F}(s^{m}),s^{r}]_{k})^{l}\in Z(% \mathfrak{R})} for every {s\in\mathfrak{R}}, then either {\mathfrak{F}(s)=ps} for every {s\in\mathfrak{R}} or {\mathfrak{R}} satisfies {s_{4}} and {\mathfrak{F}(s)=sp} for every {s\in\mathfrak{R}} and {p\in\mathfrak{U}}, the Utumi quotient ring of {\mathfrak{R}}. As an application, we prove that any spectrally generalized derivation on a semisimple Banach algebra satisfying the above mentioned differential identity must be a left multiplication map.

scholarly journals Correction to: Prime ideals and generalized derivations with central values on rings

2020 ◽  
Author(s):  
Mamouni Abdellah ◽  
Oukhtite Lahcen ◽  
Zerra Mohammed
Keyword(s):  
Prime Ideals ◽  
Generalized Derivations ◽  
Central Values

scholarly journals Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras

2009 ◽  
Vol 122 ◽  
pp. 171-190 ◽  
Author(s):  
Feng Wei ◽  
Zhankui Xiao
Keyword(s):  
Banach Algebras ◽  
Generalized Derivations ◽  
Prime Rings

Identities with Generalized Derivations in Prime Rings

2011 ◽  
Vol 9 (4) ◽  
pp. 847-863 ◽  
Author(s):  
Maja Fošner ◽  
Joso Vukman
Keyword(s):  
Generalized Derivations ◽  
Prime Rings

scholarly journals σ- ideals and generalized derivations in σ-prime rings

2013 ◽  
Vol 31 (2) ◽  
pp. 113
Author(s):  
M. Rais Khan ◽  
Deepa Arora ◽  
M. Ali Khan
Keyword(s):  
Prime Ring ◽  
Generalized Derivations ◽  
Prime Rings

Let R be a prime ring and F and G be generalized derivations of R with associated derivations d and g respectively. In the present paper, we shall investigate the commutativity of R admitting generalized derivations F and G satisfying any one of the properties: (i) F(x)x = x G(x), (ii) F(x2) = x2 , (iii) [F(x), y] = [x, G(y)], (iv) d(x)F(y) = xy, (v) F([x, y]) = [F(x), y] + [d(y), x] and (vi) F(x ◦ y) = F(x) ◦ y − d(y) ◦ x for all x, y in some appropriate subset of R.

scholarly journals Multiplicative (generalized)-derivations of prime rings that act as $n$-(anti)homomorphisms

2020 ◽  
Vol 53 (2) ◽  
pp. 125-133
Author(s):  
G.S. Sandhu
Keyword(s):  
Prime Ring ◽  
Generalized Derivations ◽  
Prime Rings ◽  
The Given

Let R be a prime ring. In this note, we describe the possible forms of multiplicative (generalized)-derivations of R that act as n-homomorphism or n-antihomomorphism on nonzero ideals of R. Consequently, from the given results one can easily deduce the results of Gusić ([7]).

Some results on ∗-differential identities in prime rings

2021 ◽  
Author(s):  
Deepak Kumar ◽  
Bharat Bhushan ◽  
Gurninder S. Sandhu
Keyword(s):  
Prime Ring ◽  
Generalized Derivation ◽  
Additive Mapping ◽  
Generalized Derivations ◽  
Prime Rings ◽  
Differential Identities ◽  
Derivation Formula

Let [Formula: see text] be a prime ring with involution ∗ of the second kind. An additive mapping [Formula: see text] is called generalized derivation if there exists a unique derivation [Formula: see text] such that [Formula: see text] for all [Formula: see text] In this paper, we investigate the structure of [Formula: see text] and describe the possible forms of generalized derivations of [Formula: see text] that satisfy specific ∗-differential identities. Precisely, we study the following situations: (i) [Formula: see text] (ii) [Formula: see text] (iii) [Formula: see text] (iv) [Formula: see text] for all [Formula: see text] Moreover, we construct some examples showing that the restrictions imposed in the hypotheses of our theorems are not redundant.

b-Generalized Derivations Acting on Multilinear Polynomials in Prime Rings

2018 ◽  
Vol 25 (04) ◽  
pp. 681-700
Author(s):  
Basudeb Dhara ◽  
Vincenzo De Filippis
Keyword(s):  
Prime Ring ◽  
Multilinear Polynomial ◽  
Extended Centroid ◽  
Generalized Derivations ◽  
Prime Rings ◽  
Ring Of Quotients ◽  
Multilinear Polynomials

Let R be a prime ring of characteristic different from 2, Q be its maximal right ring of quotients, and C be its extended centroid. Suppose that [Formula: see text] is a non-central multilinear polynomial over C, [Formula: see text], and F, G are two b-generalized derivations of R. In this paper we describe all possible forms of F and G in the case [Formula: see text] for all [Formula: see text] in Rn.

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