KnowraLocal ringLinked fromLinked fromThe 7 pages that link to Local ring, each with the reason it gives.All 7Broader topic 1Related 3Narrower topic 2Compared with 1Commutative algebraBroader topic: Local rings capture algebra near one point of a spectrum.Boolean ringCompared with: A nonzero Boolean ring is local only when it has exactly two elements.Nakayama's lemmaNarrower topic: The theorem’s local form uses this unique maximal ideal to force a finite module to vanish.Krull's principal ideal theoremRelated: After localization, the prime under study becomes the unique maximal ideal.Weierstrass preparation theoremNarrower topic: Power-series germs form local rings in which units are precisely series nonzero at the origin.Krull's theoremRelated: The theorem guarantees that the unique maximal ideal defining a local ring exists as an ideal.Homological conjectures in commutative algebraRelated: Many conjectures are formulated for local rings, where dimension and depth can be compared.