Geodesic
On Certain Decompositions of Solvable Lie Algebras
Journal of Lie theory, Tome 24 (2014) no. 4, pp. 969-978.

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The author has previously shown that solvable Lie A-algebras and complemented solvable Lie algebras decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. However, neither of these classes is contained in the other. The object of this paper is to find a larger class of algebras, containing each of these classes, in which these same results hold.
Classification : 17B05, 17B20, 17B30, 17B50
Mots-clés : Lie algebras, solvable, completely completely solvable, A-algebras, complemented, splitting, monolithic, Frattini ideal 
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     author = {D. A. Towers },
     title = {On {Certain} {Decompositions} of {Solvable} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
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     number = {4},
     year = {2014},
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}
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D. A. Towers . On Certain Decompositions of Solvable Lie Algebras. Journal of Lie theory, Tome 24 (2014) no. 4, pp. 969-978. http://geodesic.mathdoc.fr/item/JLT_2014_24_4_JLT_2014_24_4_a3/