Abstract:
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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