KnowraMaximal elementLinked fromLinked fromThe 8 pages that link to Maximal element, each with the reason it gives.All 8Broader topic 2Related 2Compared with 4Zorn's lemmaBroader topic: This is the conclusion Zorn's lemma guarantees, without requiring a greatest element.UltrafilterRelated: Maximality among proper filters yields the decisive partition-selection property.Hasse diagramRelated: Maximal elements appear at the top boundary, though several may occur.Minimal elementCompared with: It reverses the direction of the defining condition for minimality.Krull's theoremCompared with: The theorem yields an ideal maximal among proper ideals, not a greatest ideal containing all others.Greatest element and least elementCompared with: A maximal element need not lie above incomparable elements, unlike a greatest element.Join and meetCompared with: A maximal upper bound need not be least, so it need not be a join.Teichmüller–Tukey lemmaBroader topic: The lemma guarantees this endpoint, which need not be a greatest element.