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- Regular_ring abstract "In commutative algebra, a regular ring is a commutative noetherian ring, such that the localization at every prime ideal is a regular local ring: that is, every such localization has the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension.Jean-Pierre Serre defines a regular ring as a commutative noetherian ring of finite global homological dimension and shows that this is equivalent to the definition above. For regular rings, Krull dimension agrees with global homological dimension.Examples of regular rings include fields (of dimension zero) and Dedekind domains. If A is regular then so is A[X], with dimension one greater than that of A.A regular ring is reduced but need not be an integral domain. For example, the product of two regular integral domains is regular, but not an integral domain.".
- Regular_ring wikiPageID "7454705".
- Regular_ring wikiPageLength "1687".
- Regular_ring wikiPageOutDegree "17".
- Regular_ring wikiPageRevisionID "616933362".
- Regular_ring wikiPageWikiLink Category:Ring_theory.
- Regular_ring wikiPageWikiLink Commutative_algebra.
- Regular_ring wikiPageWikiLink Dedekind_domain.
- Regular_ring wikiPageWikiLink Elliptic_algebra.
- Regular_ring wikiPageWikiLink Gelfand–Kirillov_dimension.
- Regular_ring wikiPageWikiLink Geometrically_regular_ring.
- Regular_ring wikiPageWikiLink Global_dimension.
- Regular_ring wikiPageWikiLink Gorenstein_ring.
- Regular_ring wikiPageWikiLink Jean-Pierre_Serre.
- Regular_ring wikiPageWikiLink Krull_dimension.
- Regular_ring wikiPageWikiLink Localization_of_a_ring.
- Regular_ring wikiPageWikiLink Noetherian_ring.
- Regular_ring wikiPageWikiLink Prime_ideal.
- Regular_ring wikiPageWikiLink Reduced_ring.
- Regular_ring wikiPageWikiLink Regular_local_ring.
- Regular_ring wikiPageWikiLink Springer_Science+Business_Media.
- Regular_ring wikiPageWikiLinkText "Regular ring".
- Regular_ring wikiPageWikiLinkText "regular ring".
- Regular_ring wikiPageWikiLinkText "regular".
- Regular_ring wikiPageUsesTemplate Template:Abstract-algebra-stub.
- Regular_ring wikiPageUsesTemplate Template:For.
- Regular_ring wikiPageUsesTemplate Template:Reflist.
- Regular_ring subject Category:Ring_theory.
- Regular_ring hypernym Ring.
- Regular_ring type AnatomicalStructure.
- Regular_ring comment "In commutative algebra, a regular ring is a commutative noetherian ring, such that the localization at every prime ideal is a regular local ring: that is, every such localization has the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension.Jean-Pierre Serre defines a regular ring as a commutative noetherian ring of finite global homological dimension and shows that this is equivalent to the definition above.".
- Regular_ring label "Regular ring".
- Regular_ring sameAs Q956273.
- Regular_ring sameAs 正則環.
- Regular_ring sameAs Reguliere_ring.
- Regular_ring sameAs m.03hfw_s.
- Regular_ring sameAs Q956273.
- Regular_ring wasDerivedFrom Regular_ring?oldid=616933362.
- Regular_ring isPrimaryTopicOf Regular_ring.