Bokut, Chen and Huang proved that every countably generated L-algebra over a cou nt able field can be embedded into a simple t wo-generated L-algebra. In this paper, we prove that every countably generated L-algebra c...Bokut, Chen and Huang proved that every countably generated L-algebra over a cou nt able field can be embedded into a simple t wo-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.展开更多
文摘Bokut, Chen and Huang proved that every countably generated L-algebra over a cou nt able field can be embedded into a simple t wo-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.
