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An Engel condition with two generalized derivations on Lie ideals of prime rings.
- Source :
-
Journal of Algebra & Its Applications . May2023, Vol. 22 Issue 5, p1-25. 25p. - Publication Year :
- 2023
-
Abstract
- Let R be a prime ring, let L be a noncentral Lie ideal of R and let g , h be two generalized derivations of R. In this paper, we characterize the structure of R and all possible forms of g and h such that [ g (x m) x n − x s h (x t) , x r ] k = 0 for all x ∈ L , where m , n , s , t , r , k are fixed positive integers. With this, several known results can be either deduced or generalized. In particular, we give a Lie ideal version of the theorem obtained by Lee and Zhou in [An identity with generalized derivations, J. Algebra Appl. 8 (2009) 307–317] and describe a more complete version of the theorem recently obtained by Dhara and De Filippis in [Engel conditions of generalized derivations on left ideals and Lie ideals in prime rings, Comm. Algebra 48 (2020) 154–167]. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LIE algebras
*ALGEBRA
*IDEALS (Algebra)
*INTEGERS
*PRIME ideals
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 22
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 162265263
- Full Text :
- https://doi.org/10.1142/S0219498823501153