Order, lattices, ordered algebraic structures Lattices: basic notions Concept
Lattice congruence
Summary
A lattice congruence is an equivalence relation on a lattice that is compatible with join and meet. Its classes can be joined and met by taking representatives, so they form a quotient lattice. The congruences of a lattice are exactly the kernels of the lattice homomorphisms defined on it. This mirrors the role of normal subgroups for groups and of ideals for rings. The congruences of a lattice form a distributive lattice themselves.
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| Tag | T782PJYVEZ |
|---|---|
| URI | m2://T782PJYVEZ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06B10, 08A30 |
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