Abstract
The main purpose of this paper is to scrutinize the deportment of generalized derivations of R satisfying some functional
Acknowledgements
The authors are deeply indebted to the learned referees for their careful reading of the manuscript and constructive comments.
References
[1] 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. Search in Google Scholar
[2] H. E. Bell and W. S. Martindale, III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987), no. 1, 92–101. 10.4153/CMB-1987-014-xSearch in Google Scholar
[3] K. Bouchannafa, M. A. Idrissi and L. Oukhtite, Relationship between the structure of a quotient ring and the behavior of certain additive mappings, Commun. Korean Math. Soc. 37 (2022), no. 2, 359–370. Search in Google Scholar
[4] I. N. Herstein, Rings with Involution, Chic. Lectures in Math., University of Chicago, Chicago, 1976. Search in Google Scholar
[5] B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147–1166. 10.1080/00927879808826190Search in Google Scholar
[6]
M. A. Idrissi and L. Oukhtite,
Structure of a quotient ring
[7] C. Lanski, Differential identities, Lie ideals, and Posner’s theorems, Pacific J. Math. 134 (1988), no. 2, 275–297. 10.2140/pjm.1988.134.275Search in Google Scholar
[8] A. Mamouni, L. Oukhtite and M. Zerra, Certain algebraic identities on prime rings with involution, Comm. Algebra 49 (2021), no. 7, 2976–2986. 10.1080/00927872.2021.1887203Search in Google Scholar
[9] A. Mamouni, L. Oukhtite and M. Zerra, Prime ideals and generalized derivations with central values on rings, Rend. Circ. Mat. Palermo (2) 70 (2021), no. 3, 1633–1643. 10.1007/s12215-020-00578-3Search in Google Scholar
[10] A. Mamouni, L. Oukhtite and M. Zerra, Some functional identities arising from derivations, Commun. Korean Math. Soc. 38 (2023), no. 1, 79–87. Search in Google Scholar
[11] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. 10.1090/S0002-9939-1957-0095863-0Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- A note on higher order Dirac operators in Clifford analysis
- Action of higher derivations on semiprime rings
- Demicompact linear operator. Essential pseudospectra and perturbation
- On the rotations and limit cycles of solutions to the basic system of equations
- On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
- A class of nontrivial simple examples of a non-D-space
- A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
- A property of the free Gaussian distribution
- The influence of c-subnormality subgroups on the structure of finite groups
- Wave propagation on hexagonal lattices
- Timelike zero mean curvature surfaces in ℝ1 4
- A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
- On corrected Simpson-type inequalities via local fractional integrals
- Sobolev regularity for a class of local fractional new maximal operators
- On the singular directions of a holomorphic mapping in P n(ℂ)
- On minimal surfaces in ℍ2 × ℝ space
- Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
- Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
- On generalized derivations in factor rings
- Remarks on generalized derivations in factor rings
Articles in the same Issue
- Frontmatter
- A note on higher order Dirac operators in Clifford analysis
- Action of higher derivations on semiprime rings
- Demicompact linear operator. Essential pseudospectra and perturbation
- On the rotations and limit cycles of solutions to the basic system of equations
- On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
- A class of nontrivial simple examples of a non-D-space
- A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
- A property of the free Gaussian distribution
- The influence of c-subnormality subgroups on the structure of finite groups
- Wave propagation on hexagonal lattices
- Timelike zero mean curvature surfaces in ℝ1 4
- A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
- On corrected Simpson-type inequalities via local fractional integrals
- Sobolev regularity for a class of local fractional new maximal operators
- On the singular directions of a holomorphic mapping in P n(ℂ)
- On minimal surfaces in ℍ2 × ℝ space
- Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
- Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
- On generalized derivations in factor rings
- Remarks on generalized derivations in factor rings