Back to Search
Start Over
Generalized derivations with nilpotent values in semiprime rings.
- Source :
-
QM - Quaestiones Mathematicae . Jun2024, Vol. 47 Issue 6, p1195-1212. 18p. - Publication Year :
- 2024
-
Abstract
- Let R be a (semi-) prime ring with extended centroid C, let f(X1, ... , Xk) be a multilinear polynomial over C in k noncommutative indeterminates which is not central-valued on R and let g be a generalized derivation of R. In this paper, we completely characterize the form of g and the structure of R such that (g(f(x1, ... , xk))m − γf(x1, ... , xk)n)s = 0 for all x1, ... , xk ∈ R, where γ ∈ C and m, n, s are fixed positive integers. Our results naturally improve and generalize the theorems obtained by Huang and Davvaz in [Generalized derivations of rings and Banach algebras, Comm. Algebra (2013); 43, 1188–1194] and the theorems recently obtained by De Filippis et al. in [Generalized derivations with nilpotent, power-central and invertible values in prime and semiprime rings, Comm. Algebra (2019); 47, 3025–3039]. Moreover, we describe a revised version of the theorem obtained by Huang in [On generalized derivations of prime and semiprime rings, Taiwanese J. Math. (2012); 16, 771–776.] [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16073606
- Volume :
- 47
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- QM - Quaestiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 177943030
- Full Text :
- https://doi.org/10.2989/16073606.2023.2283137