Order, lattices, ordered algebraic structures Lattices: basic notions Concept
Order filter
Summary
A filter of a partially ordered set is a nonempty subset that is closed upward. Moreover, any two of its elements have a common lower bound inside it. In a lattice this means: closed upward and closed under meets. Filters are the order duals of lattice ideals. A filter on a set is a proper order filter in the lattice of subsets of .
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| Tag | Z15FXM9WM1 |
|---|---|
| URI | m2://Z15FXM9WM1 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A06, 06B10 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Prime ideal of a lattice
- Ultrafilter on a Boolean algebra
- Prime ideal theorem for distributive lattices
- Priestley duality