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

Author(s):  
Md Hamidur RAHAMAN

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Shakir Ali ◽  
Husain Alhazmi ◽  
Abdul Nadim Khan ◽  
Mohd Arif Raza

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.



2019 ◽  
Vol 45 (6) ◽  
pp. 1805-1819
Author(s):  
Shakir Ali ◽  
Basudeb Dhara ◽  
Brahim Fahid ◽  
Mohd Arif Raza


Author(s):  
Asma Ali ◽  
◽  
Shahoor Khan ◽  
Khalid Hamdin




1959 ◽  
Author(s):  
Jack Morell Anderson
Keyword(s):  






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


2011 ◽  
Vol 9 (4) ◽  
pp. 847-863 ◽  
Author(s):  
Maja Fošner ◽  
Joso Vukman


2016 ◽  
Vol 14 (1) ◽  
pp. 543-544 ◽  
Author(s):  
Ivan Kaygorodov ◽  
Yury Popov


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