Geodesic
On special Lie algebras having a~faithful module with Krull dimension
Izvestiya. Mathematics , Tome 81 (2017) no. 1, pp. 91-98

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For special Lie algebras we prove an analogue of Markov's theorem on $\mathrm{PI}$-algebras having a faithful module with Krull dimension: the solubility of the prime radical. We give an example of a semiprime Lie algebra that has a faithful module with Krull dimension but cannot be represented as a subdirect product of finitely many prime Lie algebras. We prove a criterion for a semiprime Lie algebra to be representable as such a subdirect product.
Keywords: special Lie algebra, prime radical of a Lie algebra, faithful module with Krull dimension. 
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     author = {O. A. Pikhtilkova and S. A. Pikhtilkov},
     title = {On special {Lie} algebras having a~faithful module with {Krull} dimension},
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O. A. Pikhtilkova; S. A. Pikhtilkov. On special Lie algebras having a~faithful module with Krull dimension. Izvestiya. Mathematics , Tome 81 (2017) no. 1, pp. 91-98. http://geodesic.mathdoc.fr/item/IM2_2017_81_1_a2/