Embedding Theorems for L-Algebras and Anti-commutative Algebras

Abstract

Bokut, Chen and Huang proved that every countably generated L-algebra over a countable field can be embedded into a simple two-generated L-algebra. In this paper, we prove that every countably generated L-algebra can be embedded into a simple two-generated L-algebra. We also prove that every anti-commutative algebra can be embedded into a simple anti-commutative algebra, and that every countably generated anti-commutative algebra can be embedded into a simple two-generated anti-commutative algebra. Finally, we prove that every anti-commutative algebra can be embedded into its universal enveloping non-associative algebra.