scholarly journals Annihilator of generalized derivations with power values in rings and Algebras

2020 ◽  
Author(s):  
Md Hamidur RAHAMAN
Keyword(s):  
Generalized Derivations ◽  
Rings And Algebras

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.

On Semi(prime) Rings and Algebras with Automorphisms and Generalized Derivations

2019 ◽  
Vol 45 (6) ◽  
pp. 1805-1819
Author(s):  
Shakir Ali ◽  
Basudeb Dhara ◽  
Brahim Fahid ◽  
Mohd Arif Raza
Keyword(s):  
Generalized Derivations ◽  
Prime Rings ◽  
Rings And Algebras

Identities with Generalized Derivations and Automorphisms on Semiprime Rings

2015 ◽  
Vol 2 (1) ◽  
pp. 24-29
Author(s):  
Asma Ali ◽  
◽  
Shahoor Khan ◽  
Khalid Hamdin
Keyword(s):  
Generalized Derivations ◽  
Semiprime Rings

Multiplicative (generalized)-derivations and left ideals in semiprime rings

2015 ◽  
Vol 6 (1078) ◽  
Author(s):  
A. Ali ◽  
B. Dhara ◽  
S. Khan
Keyword(s):  
Generalized Derivations ◽  
Semiprime Rings

Network rings and algebras

1959 ◽  
Author(s):  
Jack Morell Anderson
Keyword(s):  
Rings And Algebras

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

GENERALIZED DERIVATIONS FOR MIXTURES USING THE VIRIAL EQUATION: APPLICATION TO FUGACITY

1995 ◽  
Vol 137 (1) ◽  
pp. 211-214
Author(s):  
K.R. HALL ◽  
G. A. IGLESIAS-SILVA
Keyword(s):  
Virial Equation ◽  
Generalized Derivations

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 Commentary to: Generalized derivations of Lie triple systems

2016 ◽  
Vol 14 (1) ◽  
pp. 543-544 ◽  
Author(s):  
Ivan Kaygorodov ◽  
Yury Popov
Keyword(s):  
Generalized Derivations ◽  
Triple Systems
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