Embedding into 2-generated simple associative (Lie) algebras. (English) Zbl 1407.16023
Summary: In this paper, by using Gröbner-Shirshov bases theories, we prove that each countably generated associative algebra (Lie algebra) can be embedded into a simple two-generated associative algebra (Lie algebra).
MSC:
| 16S15 | Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) |
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 17B01 | Identities, free Lie (super)algebras |
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