Cohen–Macaulay ring
In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality. Under mild assumptions, a local ring is Cohen–Macaulay exactly when it is a finitely generated free module over a regular local subring. Cohen–Macaulay rings play a central role in commutative algebra: they form a very broad class, and yet they are well understood in many ways. For Noetherian local rings, there is the following chain of inclusions.
known for
Arf ringAuslander–Buchsbaum formulaBuchsbaum ringCaroline KlivansCatenary ringChevalley–Shephard–Todd theoremCohenCohen-MacaulayCohen-Macaulay local ringCohen-Macaulay moduleCohen-Macaulay ringCohen-Macaulay schemeCohen-MacauleyCohen–MacaulayCohen–Macaulay local ringCohen–Macaulay moduleCohen–Macaulay ringCohen–Macaulay schemeCoherent dualityCombinatorial commutative algebraCommutative algebraCommutative ringCraig HunekeDavid EisenbudDepth (ring theory)Derived categoryDimension theory (algebra)Dualizing moduleDualizing sheafEquidimensionalityFlat morphismFrancis Sowerby MacaulayGeneralized Cohen–Macaulay ringGlossary of algebraic geometryGlossary of commutative algebraGorenstein ringGorenstein schemeGrothendieck local dualityHironaka decompositionHochster–Roberts theorem
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Cohen–Macaulay ring
In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality. Under mild assumptions, a local ring is Cohen–Macaulay exactly when it is a finitely generated free module over a regular local subring. Cohen–Macaulay rings play a central role in commutative algebra: they form a very broad class, and yet they are well understood in many ways. For Noetherian local rings, there is the following chain of inclusions.
has abstract
Im mathematischen Teilgebiet d ...... ils siehe Kommutative Algebra.
@de
In matematica, in particolare ...... i serie formali (Cohen, 1946).
@it
In mathematics, a Cohen–Macaul ...... on rings ⊃ regular local rings
@en
У комутативній алгебрі кільцям ...... кого математика Ірвінга Коена.
@uk
在交換代數中，Cohen-Macaulay環是對應到一類代數 ...... 的情形；事實上所有Cohen-Macaulay環都具純粹性。
@zh
数学において、コーエン・マコーレー環 (英: Cohen–M ...... ン・マコーレー環 ⊃ ゴレンシュタイン環 ⊃ ⊃ 正則局所環
@ja
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author
V.I. Danilov
@en
authorlink
Francis Sowerby Macaulay
@en
Irvin S. Cohen
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first
Francis Sowerby
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Irvin
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id
c/c022970
@en
last
Cohen
@en
Macaulay
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title
Cohen–Macaulay ring
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wikiPageUsesTemplate
hypernym
comment
Im mathematischen Teilgebiet d ...... in Cohen und Francis Macaulay.
@de
In matematica, in particolare ...... i serie formali (Cohen, 1946).
@it
In mathematics, a Cohen–Macaul ...... following chain of inclusions.
@en
У комутативній алгебрі кільцям ...... кого математика Ірвінга Коена.
@uk
在交換代數中，Cohen-Macaulay環是對應到一類代數 ...... 的情形；事實上所有Cohen-Macaulay環都具純粹性。
@zh
数学において、コーエン・マコーレー環 (英: Cohen–M ...... ン・マコーレー環 ⊃ ゴレンシュタイン環 ⊃ ⊃ 正則局所環
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label
Anello di Cohen-Macaulay
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Cohen-Macaulay-Ring
@de
Cohen–Macaulay ring
@en
Кільце Коена — Маколея
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コーエン・マコーレー環
@ja
科恩-麥考利環
@zh
코언-매콜리 환
@ko