KnowraMaximal idealLinked fromLinked fromThe 15 pages that link to Maximal ideal, each with the reason it gives.All 15Broader topic 6Related 6Compared with 3Ideal (ring theory)Broader topic: It is distinguished by maximality rather than the product test defining prime ideals.Zorn's lemmaBroader topic: Applying Zorn's lemma to proper ideals proves that every nonzero unital commutative ring has a maximal ideal.IdealBroader topic: Maximal ideals classify residue fields and local algebraic behavior.Maximal elementBroader topic: It is maximality in the partially ordered set of proper ideals ordered by inclusion.Krull's theoremBroader topic: This is precisely the object whose existence Krull's theorem guarantees.Teichmüller–Tukey lemmaBroader topic: The lemma can extend a proper ideal to a maximal one because properness is preserved by chain unions.