General algebraic systems Terms, identities and equational logic Concept
Finitely based algebra
Summary
An algebra is finitely based when all of its identities follow from finitely many of them, that is, when it has a finite equational basis. Every finite group, every finite ring and every finite lattice is finitely based, but some finite algebras are not. Deciding which finite algebras are finitely based is the subject of Tarski's finite basis problem.
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| Tag | YGYZAQ12MZ |
|---|---|
| URI | m2://YGYZAQ12MZ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08B05 |
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Results about this
- Park's conjecture
- Baker's finite basis theorem
- Oates–Powell theorem
- Tarski's finite basis problem
- McKenzie's undecidability of the finite basis problem