General algebraic systems Mal'cev conditions Concept
Congruence-permutable variety
Summary
A congruence-permutable variety is a variety in which any two congruences of any algebra permute under relational composition. Groups, rings, modules and quasigroups form congruence-permutable varieties, while lattices and semilattices do not. Congruence permutability makes the congruence lattices modular and gives strong control of direct and subdirect products.
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| Tag | 1B3N9T68YV |
|---|---|
| URI | m2://1B3N9T68YV |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08B05, 08A30 |
| Specializes | Variety of algebras |
| Changed | 2 November 2026 |
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