KnowraCommutative ringLinked fromLinked fromThe 16 pages that link to Commutative ring, each with the reason it gives.All 16Broader topic 1Related 4Narrower topic 8Compared with 3Field (mathematics)Narrower topic: A field is a commutative ring in which every nonzero element is invertible.Polynomial ringRelated: Commutativity of the coefficient ring affects factorization and many familiar polynomial results.Formal power seriesNarrower topic: Formal series inherit their coefficient arithmetic from a commutative ring.Ring (mathematics)Broader topic: This common subclass adds symmetry absent from general ring multiplication.Commutative algebraNarrower topic: These rings are the central objects commutative algebra investigates.FieldRelated: Commutativity is part of the ring structure required in the definition of a field.IdealCompared with: Commutativity permits equivalent left- and right-multiplication closure.Division ringCompared with: Commutative division rings are precisely fields, so dropping commutativity enlarges the concept.Boolean ringRelated: Boolean rings are commutative, even when commutativity is not assumed in the definition.Local ringNarrower topic: The usual local-ring theory in algebraic geometry specializes the broader class of commutative rings.Hilbert's basis theoremNarrower topic: The theorem is usually stated for commutative coefficient rings and their polynomial rings.Ring theoryCompared with: Commutativity separates the setting of much classical theory from broader ring theory.Freshman's dreamNarrower topic: The identity is stated for this setting, where the binomial theorem applies.Krull's theoremNarrower topic: Commutativity is part of the theorem's stated setting.Sophie Germain's identityNarrower topic: Polynomial identities such as this hold across commutative rings, though factor properties depend on the ring.Unit (ring theory)Related: In a commutative ring, the inverse condition is simply a product equal to one.
KnowraCommutative ringLinked fromLinked fromThe 16 pages that link to Commutative ring, each with the reason it gives.All 16Broader topic 1Related 4Narrower topic 8Compared with 3Field (mathematics)Narrower topic: A field is a commutative ring in which every nonzero element is invertible.Polynomial ringRelated: Commutativity of the coefficient ring affects factorization and many familiar polynomial results.Formal power seriesNarrower topic: Formal series inherit their coefficient arithmetic from a commutative ring.Ring (mathematics)Broader topic: This common subclass adds symmetry absent from general ring multiplication.Commutative algebraNarrower topic: These rings are the central objects commutative algebra investigates.FieldRelated: Commutativity is part of the ring structure required in the definition of a field.IdealCompared with: Commutativity permits equivalent left- and right-multiplication closure.Division ringCompared with: Commutative division rings are precisely fields, so dropping commutativity enlarges the concept.Boolean ringRelated: Boolean rings are commutative, even when commutativity is not assumed in the definition.Local ringNarrower topic: The usual local-ring theory in algebraic geometry specializes the broader class of commutative rings.Hilbert's basis theoremNarrower topic: The theorem is usually stated for commutative coefficient rings and their polynomial rings.Ring theoryCompared with: Commutativity separates the setting of much classical theory from broader ring theory.Freshman's dreamNarrower topic: The identity is stated for this setting, where the binomial theorem applies.Krull's theoremNarrower topic: Commutativity is part of the theorem's stated setting.Sophie Germain's identityNarrower topic: Polynomial identities such as this hold across commutative rings, though factor properties depend on the ring.Unit (ring theory)Related: In a commutative ring, the inverse condition is simply a product equal to one.