Abstract
In this work, the subject of ideal in a semiprime ring with multiplicative (generalized)- reverse derivations studied is included. We give new essential results for researchers in this field and generalize some results found in the literature. Also, the application of continuous reverse derivations in Banach algebras is discussed for the first time.
References
[1] H. E. Bell and L.-C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar. 53 (1989), no. 3–4, 339–346. 10.1007/BF01953371Search 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] 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/S0161171292000255Search in Google Scholar
[4] M. N. Daif and M. S. Tammam El-Sayiad, Multiplicative generalized derivations which are additive, East-West J. Math. 9 (2007), no. 1, 31–37. 10.12988/ija.2007.07060Search in Google Scholar
[5] I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104–1110. 10.1090/S0002-9939-1957-0095864-2Search in Google Scholar
[6] B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067–1073. 10.2307/2373290Search in Google Scholar
[7] P. H. Lee and T. K. Lee, On derivations of prime rings, Chinese J. Math. 9 (1981), no. 2, 107–110. Search in Google Scholar
[8] A. M. Sinclair, Continuous derivations on Banach algebras, Proc. Amer. Math. Soc. 20 (1969), 166–170. 10.1090/S0002-9939-1969-0233207-XSearch in Google Scholar
[9] I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260–264. 10.1007/BF01362370Search in Google Scholar
[10] M. P. Thomas, The image of a derivation is contained in the radical, Ann. of Math. (2) 128 (1988), no. 3, 435–460. 10.2307/1971432Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- The Wigner transformation associated with the Hankel multidimensional operator
- Index for generalized Fredholm operators and generalized perturbation theory
- One-radius theorem for harmonic tempered distributions
- Optimal convergence factors for general Fourier coefficients
- Natural transformations for quasigroupoids
- Numerical solution for a nonlinear diffusion model with source terms
- Multiplicative (generalized)-reverse derivations in rings and Banach algebras
- Variational approach of p-Laplacian impulsive differential equations with periodic conditions
- Solvable groups with four conjugacy classes outside a normal subgroup
- Quadratic-phase orthonormal wavelets
- Uncertainty inequality on weighted Hardy spaces
- Faithful representations of the Galilean Lie algebra in two spatial dimensions
- Weighted composition operators from Dirichlet–Zygmund-type spaces into Stević-type spaces
Articles in the same Issue
- Frontmatter
- The Wigner transformation associated with the Hankel multidimensional operator
- Index for generalized Fredholm operators and generalized perturbation theory
- One-radius theorem for harmonic tempered distributions
- Optimal convergence factors for general Fourier coefficients
- Natural transformations for quasigroupoids
- Numerical solution for a nonlinear diffusion model with source terms
- Multiplicative (generalized)-reverse derivations in rings and Banach algebras
- Variational approach of p-Laplacian impulsive differential equations with periodic conditions
- Solvable groups with four conjugacy classes outside a normal subgroup
- Quadratic-phase orthonormal wavelets
- Uncertainty inequality on weighted Hardy spaces
- Faithful representations of the Galilean Lie algebra in two spatial dimensions
- Weighted composition operators from Dirichlet–Zygmund-type spaces into Stević-type spaces