On b-generalized skew derivations having centralizing commutator in prime rings

2022 ◽  
pp. 1-10
Author(s):  
Balchand Prajapati ◽  
Charu Gupta
Keyword(s):  
Prime Rings

Lie Ideals and Jordan q-Centralizers of Prime Rings

2011 ◽  
Vol 14 (2) ◽  
pp. 172-177
Author(s):  
Abdulrahman H. Majeed ◽  
◽  
Mushreq I. Meften ◽  
Keyword(s):  
Prime Rings

Derivations of differentially semiprime rings

2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee
Keyword(s):  
Commutative Ring ◽  
Semiprime Ring ◽  
Prime Rings ◽  
Commutative Case ◽  
Lie Ring ◽  
Lie Rings ◽  
Semiprime Rings ◽  
Torsion Free

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

m-potent commutators involving skew derivations and multilinear polynomials

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammad Ashraf ◽  
Sajad Ahmad Pary ◽  
Mohd Arif Raza
Keyword(s):  
Prime Ring ◽  
Quotient Ring ◽  
Multilinear Polynomial ◽  
Extended Centroid ◽  
Prime Rings ◽  
Skew Derivation ◽  
Martindale Quotient Ring ◽  
Multilinear Polynomials ◽  
The Right ◽  
The Relationship

AbstractLet {\mathscr{R}} be a prime ring, {\mathscr{Q}_{r}} the right Martindale quotient ring of {\mathscr{R}} and {\mathscr{C}} the extended centroid of {\mathscr{R}}. In this paper, we discuss the relationship between the structure of prime rings and the behavior of skew derivations on multilinear polynomials. More precisely, we investigate the m-potent commutators of skew derivations involving multilinear polynomials, i.e.,\big{(}[\delta(f(x_{1},\ldots,x_{n})),f(x_{1},\ldots,x_{n})]\big{)}^{m}=[% \delta(f(x_{1},\ldots,x_{n})),f(x_{1},\ldots,x_{n})],where {1<m\in\mathbb{Z}^{+}}, {f(x_{1},x_{2},\ldots,x_{n})} is a non-central multilinear polynomial over {\mathscr{C}} and δ is a skew derivation of {\mathscr{R}}.

On Lie Ideals and Automorphisms in Prime Rings

2020 ◽  
Vol 107 (1-2) ◽  
pp. 140-144
Author(s):  
N. Rehman
Keyword(s):  
Prime Rings

On additive maps of prime rings satisfying the engel condition

1997 ◽  
Vol 25 (12) ◽  
pp. 3889-3902 ◽  
Author(s):  
K.L Beidar ◽  
Y Fong ◽  
P.-H Lee ◽  
T.-L Wong
Keyword(s):  
Prime Rings ◽  
Engel Condition ◽  
Additive Maps

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

A note on generalized Lie derivations of prime rings

2016 ◽  
Vol 12 (1) ◽  
pp. 247-260
Author(s):  
Nihan Baydar Yarbil ◽  
Nurcan Argaç
Keyword(s):  
Prime Rings ◽  
Lie Derivations

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.

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