General algebraic systems Quasivarieties and model classes Concept
Pseudovariety
Summary
A pseudovariety is a class of finite algebras of one signature that is closed under homomorphic images, subalgebras and finite direct products. It is the analogue of a variety for finite algebras. Pseudovarieties are not always defined by identities, but Reiterman's theorem shows that they are defined by pseudoidentities. Pseudovarieties of finite semigroups and monoids classify regular languages in algebraic automata theory.
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| Tag | XR4DPKX7T1 |
|---|---|
| URI | m2://XR4DPKX7T1 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08B99, 20M07 |
| Changed | 2 November 2026 |
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