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- Title
On skew-commuting generalized skew derivations in prime and semiprime rings.
- Authors
Carini, Luisa; De Filippis, Vincenzo
- Abstract
Let R be a noncommutative prime ring of characteristic different from 2 , with right Martindale quotient ring Q r and extended centroid C. Let m , n ≥ 1 be fixed integers and F a nonzero generalized skew derivation of R. In this paper, we investigate the set S = { F (x m) x n + x n F (x m) : x ∈ R } and prove that its left annihilator in R is identically zero. Using the above result, we also study the identity F (x) x n + x n F (x) = 0 for semiprime rings.
- Subjects
NONCOMMUTATIVE rings; QUOTIENT rings; CENTROID; INTEGERS
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 8, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498824502116