A note on b-generalized (α,β)-derivations in prime rings
-
Nripendu Bera
und
Basudeb Dhara
Abstract
Let R be a prime ring, let
for all
Funding statement: Second author is supported by a grant from Science and Engineering Research Board (SERB), New Delhi, India. Grant No. is MTR/2022/000568.
Acknowledgements
We are highly thankful to the referee whose comments and suggestions enhanced the paper and made it more readable.
References
[1] E. Albaş, Generalized derivations on ideals of prime rings, Miskolc Math. Notes 14 (2013), no. 1, 3–9. 10.18514/MMN.2013.499Suche in Google Scholar
[2] A. Ali, V. De Filippis and F. Shujat, On one sided ideals of a semiprime ring with generalized derivations, Aequationes Math. 85 (2013), no. 3, 529–537. 10.1007/s00010-012-0150-1Suche in Google Scholar
[3]
F. Ali and M. A. Chaudhry,
On generalized
[4] M. Ashraf, A. Ali and S. Ali, Some commutativity theorems for rings with generalized derivations, Southeast Asian Bull. Math. 31 (2007), no. 3, 415–421. Suche in Google Scholar
[5] M. Ashraf, A. Ali and R. Rani, On generalized derivations of prime rings, Southeast Asian Bull. Math. 29 (2005), no. 4, 669–675. Suche in Google Scholar
[6] M. Ashraf and N. ur Rehman, On derivation and commutativity in prime rings, East-West J. Math. 3 (2001), no. 1, 87–91. Suche in Google Scholar
[7] M. N. Daif and H. E. Bell, Remarks on derivations on semiprime rings, Internat. J. Math. Math. Sci. 15 (1992), no. 1, 205–206. 10.1155/S0161171292000255Suche in Google Scholar
[8]
V. De Filippis and F. Wei,
b-generalized
[9] B. Dhara, Remarks on generalized derivations in prime and semiprime rings, Int. J. Math. Math. Sci. 2010 (2010), Article ID 646587. 10.1155/2010/646587Suche in Google Scholar
[10] B. Dhara, Generalized derivations acting as a homomorphism or anti-homomorphism in semiprime rings, Beitr. Algebra Geom. 53 (2012), no. 1, 203–209. 10.1007/s13366-011-0051-9Suche in Google Scholar
[11] B. Dhara, S. Kar and N. Bera, Some identities related to multiplicative (generalized)-derivations in prime and semiprime rings, Rend. Circ. Mat. Palermo (2) 72 (2023), no. 2, 1497–1516. 10.1007/s12215-022-00743-wSuche in Google Scholar
[12] B. Dhara, S. Kar and S. Mondal, A result on generalized derivations on Lie ideals in prime rings, Beitr. Algebra Geom. 54 (2013), no. 2, 677–682. 10.1007/s13366-012-0128-0Suche in Google Scholar
[13]
B. Dhara, S. Kar and S. Mondal,
Commutativity theorems on prime and semiprime rings with generalized
[14] B. Dhara, S. Kar and K. G. Pradhan, Generalized derivations acting as homomorphism or anti-homomorphism with central values in semiprime rings, Miskolc Math. Notes 16 (2015), no. 2, 781–791. 10.18514/MMN.2015.1507Suche in Google Scholar
[15]
C. Garg and R. K. Sharma,
On generalized
[16] B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147–1166. 10.1080/00927879808826190Suche in Google Scholar
[17]
Y.-S. Jung and K.-H. Park,
On generalized
[18]
H. Marubayashi, M. Ashraf, N.-u. Rehman and S. Ali,
On generalized
[19] S. K. Tiwari, R. K. Sharma and B. Dhara, Identities related to generalized derivation on ideal in prime rings, Beitr. Algebra Geom. 57 (2016), no. 4, 809–821. 10.1007/s13366-015-0262-6Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Numerical approaches for solution of hyperbolic difference equations on circle
- A note on b-generalized (α,β)-derivations in prime rings
- Analytic solution to functional differential equations via Bell’s polynomials
- Floquet theory and stability for a class of first order differential equations with delays
- Representations of a number in an arbitrary base with unbounded digits
- V_a -deformed free convolution and variance function
- Generalized essential spectra involving the class of g-g-Riesz operators
- On perturbation of continuous frames in Hilbert C *-modules
- Almost measurable functions on probability spaces
- On φ-u-S-flat modules and nonnil-u-S-injective modules
- Busemann--Petty-type problem for μ-intersection bodies
- On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition
- A generalization of Hardy’s inequality to infinite tensors
- A note on maximal estimate for an oscillatory operator
- Some summation theorems and transformations for hypergeometric functions of Kampé de Fériet and Srivastava
- On the correspondence between periodic solutions of differential and dynamic equations on periodic time scales
Artikel in diesem Heft
- Frontmatter
- Numerical approaches for solution of hyperbolic difference equations on circle
- A note on b-generalized (α,β)-derivations in prime rings
- Analytic solution to functional differential equations via Bell’s polynomials
- Floquet theory and stability for a class of first order differential equations with delays
- Representations of a number in an arbitrary base with unbounded digits
- V_a -deformed free convolution and variance function
- Generalized essential spectra involving the class of g-g-Riesz operators
- On perturbation of continuous frames in Hilbert C *-modules
- Almost measurable functions on probability spaces
- On φ-u-S-flat modules and nonnil-u-S-injective modules
- Busemann--Petty-type problem for μ-intersection bodies
- On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition
- A generalization of Hardy’s inequality to infinite tensors
- A note on maximal estimate for an oscillatory operator
- Some summation theorems and transformations for hypergeometric functions of Kampé de Fériet and Srivastava
- On the correspondence between periodic solutions of differential and dynamic equations on periodic time scales
