General algebraic systems Mal'cev conditions Concept
Congruence-distributive variety
Summary
A congruence-distributive variety is a variety in which the congruence lattice of every algebra is a distributive lattice. Lattices, Boolean algebras and Heyting algebras form congruence-distributive varieties, while groups do not. In such a variety, Jónsson's lemma locates all subdirectly irreducible algebras, which makes the variety much easier to describe.
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| Tag | 9GZ7F6ETC6 |
|---|---|
| URI | m2://9GZ7F6ETC6 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08B10 |
| Specializes | Variety of algebras |
| Changed | 2 November 2026 |
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