Abstract & Pure

Learn Universal Algebra

What survives when you stop naming the operations: signatures and algebras, subuniverses and generation, congruences and the congruence lattice, subdirect products and Birkhoff's representation theorem, terms and free algebras, the HSP theorem, equational logic and its completeness, clones and polynomial operations, Mal'cev conditions, Jónsson terms and congruence distributivity, congruence modularity, the lattice of subvarieties, quasivarieties, polymorphisms and the constraint satisfaction dichotomy, the finite basis problem, and the commutator.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

18 lessons in Universal Algebra

Signatures, algebras and homomorphismsSubuniverses and generationCongruences and quotient algebrasThe congruence latticeDirect and subdirect productsSubdirectly irreducible algebrasTerms and free algebrasVarieties and the HSP theoremEquational logic and completenessClones, term and polynomial operationsMal'cev conditions and permutabilityJónsson terms and congruence distributivityCongruence modularityThe lattice of subvarietiesQuasivarietiesPolymorphisms and the CSP dichotomyThe finite basis problemThe commutator and abelian algebras
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Universal Algebra exactly where it's useful.

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