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

Generalized Derivations with Power-Central Values on Multilinear Polynomials

2006 ◽  
Vol 13 (03) ◽  
pp. 405-410 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Commutative Ring ◽  
Generalized Derivation ◽  
Multilinear Polynomial ◽  
Extended Centroid ◽  
Generalized Derivations ◽  
Prime Algebra ◽  
Standard Identity ◽  
Central Values ◽  
Multilinear Polynomials ◽  
Power Central

Let R be a prime algebra over a commutative ring K, Z and C the center and extended centroid of R, respectively, g a generalized derivation of R, and f (X1, …,Xt) a multilinear polynomial over K. If g(f (X1, …,Xt))n ∈ Z for all x1, …, xt ∈ R, then either there exists an element λ ∈ C such that g(x)= λx for all x ∈ R or f(x1, …,xt) is central-valued on R except when R satisfies s4, the standard identity in four variables.

scholarly journals Generalized derivations acting as homomorphism or anti-homomorphism with central values in semiprime rings

2015 ◽  
Vol 16 (2) ◽  
pp. 781-791 ◽  
Author(s):  
Basudeb Dhara ◽  
Sukhendu Kar ◽  
Krishna Gopal Pradahan
Keyword(s):  
Generalized Derivations ◽  
Central Values ◽  
Semiprime Rings

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.

N-ideals of commutative rings

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2933-2941 ◽  
Author(s):  
Unsal Tekir ◽  
Suat Koc ◽  
Kursat Oral
Keyword(s):  
Commutative Ring ◽  
Commutative Rings ◽  
Proper Ideal ◽  
Prime Ideals ◽  
Nonzero Identity

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ? I with a ? ?0, then b ? I for every a,b ? R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.

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