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In this paper https://link.springer.com/content/pdf/10.1007/BF01877233.pdf, there is a corollary about embedding of countable associate algebras in a simple associative algebra with three generators. (Corollary #1). May you help me to sort out this result and the proof of that. My confusion is about embedding in three generated algebras. As we know there is a result for Lie algebras stating that Every finite- or countable-dimensional Lie algebra can be embedded in a Lie algebra generated by two elements.

Nil
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  • In this paper, I know about Composition method , but I do not know what are $K1, K2, K3$. Do they mean that $K1, K2, K3$ are generated by one element? In the case of Lie algebras, we can embed Lie algebras in two generated Lie algebras? Can it be investigated for associative algebras? – Nil Aug 09 '19 at 16:59

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