About embedding associative algebras

Question

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.