Abstract
Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f, d : R → A are linear maps satisfying thatf ([x, y]) = f (x) y - f (y) x + xd (y) - yd (x) for all x, y ∈ R,then there exist a generalized derivation g : B → AC + C and a linear map ζ : R → C such that f (x) = g (x) + ζ (x) for all x ∈ R and ζ ([R, R]) = 0 provided that A does not satisfy the standard identity of degree 18.
Original language | English |
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Pages (from-to) | 1236-1242 |
Number of pages | 7 |
Journal | Linear Algebra and Its Applications |
Volume | 430 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2009 Feb 1 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics