Geodesic
On action of outer derivations on nilpotent ideals of Lie algebras
Algebra and discrete mathematics, no. 1 (2009), pp. 74-82

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Action of outer derivations on nilpotent ideals of Lie algebras are considered. It is shown that for a nilpotent ideal $I$ of a Lie algebra $L$ over a field $F$ the ideal $I+D(I)$ is nilpotent, provided that $char F=0$ or $I$ nilpotent of nilpotency class less than $p-1$, where $p=char F$. In particular, the sum $N(L)$ of all nilpotent ideals of a Lie algebra $L$ is a characteristic ideal, if $char F=0$ or $N(L)$ is nilpotent of class less than $p-1$, where $p=char F$.
Keywords: Lie algebra, derivation, nilpotent ideal.
Mots-clés : solvable radical 
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     author = {Dmitriy V. Maksimenko},
     title = {On action of outer derivations on nilpotent ideals of {Lie} algebras},
     journal = {Algebra and discrete mathematics},
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     number = {1},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2009_1_a7/}
}
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Dmitriy V. Maksimenko. On action of outer derivations on nilpotent ideals of Lie algebras. Algebra and discrete mathematics, no. 1 (2009), pp. 74-82. http://geodesic.mathdoc.fr/item/ADM_2009_1_a7/