Revision #190 → #1339 · back to history
addedKrull dimensiona9f0377462c0
addedKrull dimension can be infinite for Noetherian rings47df4159fb46
addedDimension of an affine variety1d05286100ec
addedField has Krull dimension 00aba2dd83de3
addedLocal ring of dimension zerod71e914771ec
addedLength of a chain of prime ideals8ef4d27f465e
addedKrull dimension (formal)cf0d617d596a
addedHeight of a prime idealf5cdc02317e9
addedHeight zero iff minimal primef0a7fecdb907
addedKrull dimension as supremum of heights831baa513bb2
addedPrime ideals have finite height in Noetherian rings34dafd1a7144
addedNoetherian ring of infinite Krull dimension (Nagata)5cf03bbdac0e
addedCatenary ringf8f1e25dfaeb
addedUniversally catenary ringf4110bafdf8b
addedNon-catenary Noetherian ring (Nagata)ec82ceacd603
addedKrull's height theorem2c64ec9c9252
addedHeight of an ideal156a190c65df
addedKrull dimension equals dimension of the spectrum31b2de77146d
addedDimension of a polynomial ring over a fieldf901bb9409b1
addedDimension of R[x] for Noetherian R963c08427f02
addedDimension of R[x] for non-Noetherian Rd24bcc5f2494
addedAn ideal of height 28ddc526b75ca
addedHeight of an irreducible-polynomial ideal2f738c8ba133
addedRing of integers has dimension 19a8f0c9e4eeb
addedPID that is not a field has dimension 1761d6f865797
addedIntegral domain is a field iff dimension zerob87cc919c122
addedDedekind domains have dimension one57509643e1c2
addedKrull dimension of the zero ring8d15d5d3dfff
addedZero ring is the only ring with negative dimension8887a623aae1
addedArtinian iff Noetherian and dimension at most zero8fb381bfbd92
addedIntegral extension preserves dimensione3a928098aeb
addedKrull dimension bounded by transcendence degree232e9e3505b4
addedEquality for finitely generated algebras325bc80d9f40
addedDimension via associated graded ring72c4c21e3b4f
addedNoetherian ring of dimension zero is a product of local rings4545808e0c0e
addedCohen–Macaulay ring598139034767
addedRegular local ring is Cohen–Macaulay394295cb77f9
addedUFD iff height 1 primes are principal7d31a00ef80a
addedEquivalent conditions for reduced dimension-zero ringse75e0e74f4f6
addedKrull dimension of a module26a7c52ee125
addedKrull dimension as deviation of poset of submodules2c7341774a35
addedAgreement of definitions for Noetherian rings1b29002c946c
addedDefinitions differ for non-Noetherian ringsc327af2a711e