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• Cohen–Macaulay_ring abstract "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.They are named for Francis Sowerby Macaulay (1916), who proved the unmixedness theorem for polynomial rings, and for Irvin Cohen (1946), who proved the unmixedness theorem for formal power series rings. All Cohen–Macaulay rings have the unmixedness property.For Noetherian local rings, there is the following chain of inclusions. Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings".
• Cohen–Macaulay_ring wikiPageExternalLink 1990313.
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• Cohen–Macaulay_ring wikiPageRevisionID "708324724".
• Cohen–Macaulay_ring wikiPageWikiLink Abelian_variety.
• Cohen–Macaulay_ring wikiPageWikiLink Affine_variety.
• Cohen–Macaulay_ring wikiPageWikiLink Algebraic_geometry.
• Cohen–Macaulay_ring wikiPageWikiLink Ample_line_bundle.
• Cohen–Macaulay_ring wikiPageWikiLink Artinian_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Associated_prime.
• Cohen–Macaulay_ring wikiPageWikiLink Cambridge_University_Press.
• Cohen–Macaulay_ring wikiPageWikiLink Canonical_singularity.
• Cohen–Macaulay_ring wikiPageWikiLink Category:Algebraic_geometry.
• Cohen–Macaulay_ring wikiPageWikiLink Category:Commutative_algebra.
• Cohen–Macaulay_ring wikiPageWikiLink Catenary_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Characteristic_(algebra).
• Cohen–Macaulay_ring wikiPageWikiLink Cohen–Macaulay_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Coherent_duality.
• Cohen–Macaulay_ring wikiPageWikiLink Coherent_sheaf.
• Cohen–Macaulay_ring wikiPageWikiLink Commutative_algebra.
• Cohen–Macaulay_ring wikiPageWikiLink Commutative_property.
• Cohen–Macaulay_ring wikiPageWikiLink Commutative_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Complete_intersection_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Completion_(algebra).
• Cohen–Macaulay_ring wikiPageWikiLink Connected_space.
• Cohen–Macaulay_ring wikiPageWikiLink Cusp_(singularity).
• Cohen–Macaulay_ring wikiPageWikiLink Depth_(ring_theory).
• Cohen–Macaulay_ring wikiPageWikiLink Derived_category.
• Cohen–Macaulay_ring wikiPageWikiLink Equidimensionality.
• Cohen–Macaulay_ring wikiPageWikiLink Field_(mathematics).
• Cohen–Macaulay_ring wikiPageWikiLink Finite_morphism.
• Cohen–Macaulay_ring wikiPageWikiLink Finitely_generated_algebra.
• Cohen–Macaulay_ring wikiPageWikiLink Finitely_generated_module.
• Cohen–Macaulay_ring wikiPageWikiLink Fixed-point_subring.
• Cohen–Macaulay_ring wikiPageWikiLink Flat_module.
• Cohen–Macaulay_ring wikiPageWikiLink Formal_power_series.
• Cohen–Macaulay_ring wikiPageWikiLink Free_module.
• Cohen–Macaulay_ring wikiPageWikiLink Gorenstein_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Graded_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Graduate_Texts_in_Mathematics.
• Cohen–Macaulay_ring wikiPageWikiLink Grothendieck_local_duality.
• Cohen–Macaulay_ring wikiPageWikiLink Hilbert–Burch_theorem.
• Cohen–Macaulay_ring wikiPageWikiLink Hochster–Roberts_theorem.
• Cohen–Macaulay_ring wikiPageWikiLink Ideal.
• Cohen–Macaulay_ring wikiPageWikiLink Integral_domain.
• Cohen–Macaulay_ring wikiPageWikiLink Integrally_closed_domain.
• Cohen–Macaulay_ring wikiPageWikiLink Krull_dimension.
• Cohen–Macaulay_ring wikiPageWikiLink Line_bundle.
• Cohen–Macaulay_ring wikiPageWikiLink Linear_algebraic_group.
• Cohen–Macaulay_ring wikiPageWikiLink Local_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Localization_of_a_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Mathematics.
• Cohen–Macaulay_ring wikiPageWikiLink Matrix_(mathematics).
• Cohen–Macaulay_ring wikiPageWikiLink Maximal_ideal.
• Cohen–Macaulay_ring wikiPageWikiLink Minimal_model_program.
• Cohen–Macaulay_ring wikiPageWikiLink Minor_(linear_algebra).
• Cohen–Macaulay_ring wikiPageWikiLink Noether_normalization_lemma.
• Cohen–Macaulay_ring wikiPageWikiLink Noetherian_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Noetherian_scheme.
• Cohen–Macaulay_ring wikiPageWikiLink Polynomial_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Prime_ideal.
• Cohen–Macaulay_ring wikiPageWikiLink Princeton_University_Press.
• Cohen–Macaulay_ring wikiPageWikiLink Projective_variety.
• Cohen–Macaulay_ring wikiPageWikiLink Rational_singularity.
• Cohen–Macaulay_ring wikiPageWikiLink Reduced_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Reductive_group.
• Cohen–Macaulay_ring wikiPageWikiLink Regular_local_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Regular_scheme.
• Cohen–Macaulay_ring wikiPageWikiLink Regular_sequence.
• Cohen–Macaulay_ring wikiPageWikiLink Robin_Hartshorne.
• Cohen–Macaulay_ring wikiPageWikiLink Scheme_(mathematics).
• Cohen–Macaulay_ring wikiPageWikiLink Serre_duality.
• Cohen–Macaulay_ring wikiPageWikiLink Smooth_scheme.
• Cohen–Macaulay_ring wikiPageWikiLink Spectrum_of_a_ring.
• Cohen–Macaulay_ring wikiPageWikiLink Springer_Science+Business_Media.
• Cohen–Macaulay_ring wikiPageWikiLink Toric_variety.
• Cohen–Macaulay_ring wikiPageWikiLink Transactions_of_the_American_Mathematical_Society.
• Cohen–Macaulay_ring wikiPageWikiLink nowiki%3Ex%3Cnowiki%3E.
• Cohen–Macaulay_ring wikiPageWikiLink sub%3E%3Cnowiki%3E.
• Cohen–Macaulay_ring wikiPageWikiLinkText "Cohen–Macaulay ring".
• Cohen–Macaulay_ring wikiPageWikiLinkText "Cohen–Macaulay local ring".
• Cohen–Macaulay_ring wikiPageWikiLinkText "Cohen–Macaulay ring".
• Cohen–Macaulay_ring wikiPageWikiLinkText "Cohen–Macaulay ring#The unmixedness theorem".
• Cohen–Macaulay_ring wikiPageWikiLinkText "Cohen–Macaulay ring#unmixed".
• Cohen–Macaulay_ring wikiPageWikiLinkText "Cohen–Macaulay".
• Cohen–Macaulay_ring wikiPageWikiLinkText "Cohen–Macaulay_ring#The_unmixedness_theorem".
• Cohen–Macaulay_ring wikiPageWikiLinkText "Macaulay".
• Cohen–Macaulay_ring author "V.I. Danilov".
• Cohen–Macaulay_ring authorlink "Francis Sowerby Macaulay".
• Cohen–Macaulay_ring authorlink "Irvin S. Cohen".
• Cohen–Macaulay_ring first "Francis Sowerby".
• Cohen–Macaulay_ring first "Irvin".
• Cohen–Macaulay_ring id "c/c022970".
• Cohen–Macaulay_ring last "Cohen".
• Cohen–Macaulay_ring last "Macaulay".
• Cohen–Macaulay_ring title "Cohen–Macaulay ring".
• Cohen–Macaulay_ring wikiPageUsesTemplate Template:Anchor.
• Cohen–Macaulay_ring wikiPageUsesTemplate Template:Citation.

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