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gptkbp:instanceOf
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commutative ring
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gptkbp:application
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gptkb:algebraic_geometry
homological algebra
singularity theory
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gptkbp:citation
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gptkb:Atiyah_&_Macdonald,_Introduction_to_Commutative_Algebra
gptkb:Matsumura,_Commutative_Ring_Theory
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gptkbp:defines
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A Noetherian ring in which the depth equals the Krull dimension.
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gptkbp:field
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gptkb:commutative_algebra
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gptkbp:generalizes
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gptkb:Gorenstein_ring
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https://www.w3.org/2000/01/rdf-schema#label
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Cohen–Macaulay ring
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gptkbp:introducedIn
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1946
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gptkbp:namedAfter
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gptkb:Francis_S._Macaulay
gptkb:Irving_S._Cohen
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gptkbp:property
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A Cohen–Macaulay ring is universally catenary.
All complete intersections are Cohen–Macaulay.
All regular local rings are Cohen–Macaulay.
All polynomial rings over a field are Cohen–Macaulay.
A quotient of a Cohen–Macaulay ring by a regular sequence is Cohen–Macaulay.
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gptkbp:relatedConcept
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gptkb:Gorenstein_ring
gptkb:Krull_dimension
gptkb:regular_ring
depth
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gptkbp:specialty
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gptkb:regular_ring
complete intersection ring
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gptkbp:bfsParent
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gptkb:commutative_algebra
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gptkbp:bfsLayer
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5
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