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 |
|---|---|
| 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 |
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All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics
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On generalized Lie derivations of Lie ideals of prime algebras. / Liao, Ping Bao; Liu, Cheng-Kai.
In: Linear Algebra and Its Applications, Vol. 430, No. 4, 01.02.2009, p. 1236-1242.Research output: Contribution to journal › Article
TY - JOUR
T1 - On generalized Lie derivations of Lie ideals of prime algebras
AU - Liao, Ping Bao
AU - Liu, Cheng-Kai
PY - 2009/2/1
Y1 - 2009/2/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=58049192816&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2008.10.022
DO - 10.1016/j.laa.2008.10.022
M3 - Article
AN - SCOPUS:58049192816
VL - 430
SP - 1236
EP - 1242
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
IS - 4
ER -