General algebraic systems Homomorphisms and substructures Concept
Subalgebra lattice
Summary
The subalgebra lattice of an algebra is the set of all its subuniverses, ordered by inclusion. It is a complete lattice, and in fact an algebraic lattice whose compact elements are the finitely generated subuniverses. It generalizes the lattice of subgroups of a group. By the Birkhoff–Frink theorem, every algebraic lattice arises in this way.
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| Tag | T0TNG7AGXT |
|---|---|
| URI | m2://T0TNG7AGXT |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08A30, 06B23 |
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