Embedding Theorems for L-Algebras and Anti-commutative Algebras

• 来源期刊: 代数集刊（英文版）
• 关键词: L-algebra anti-commutative algebra Gr(o)bner-Shirshov basis
• 年，卷（期）: 2019,（1）
• 页码范围: 51-64
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386719000063

摘要

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.