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- Catenary_ring abstract "In mathematics, a commutative ring R is catenary if for any pair of prime ideals p, q,any two strictly increasing chains p=p0 ⊂p1 ... ⊂pn= q of prime idealsare contained in maximal strictly increasing chains from p to q of the same (finite) length. In a geometric situation, in which the dimension of an algebraic variety attached to a prime ideal will decrease as the prime ideal becomes bigger, the length of such a chain n is usually the difference in dimensions.A ring is called universally catenary if all finitely generated algebras over it are catenary rings.The word 'catenary' is derived from the Latin word catena, which means "chain".There is the following chain of inclusions. Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings".
- Catenary_ring wikiPageExternalLink 1118799769.
- Catenary_ring wikiPageID "10034460".
- Catenary_ring wikiPageLength "4905".
- Catenary_ring wikiPageOutDegree "15".
- Catenary_ring wikiPageRevisionID "662446494".
- Catenary_ring wikiPageWikiLink Category:Algebraic_geometry.
- Catenary_ring wikiPageWikiLink Category:Commutative_algebra.
- Catenary_ring wikiPageWikiLink Cohen-Macaulay_ring.
- Catenary_ring wikiPageWikiLink Cohen–Macaulay_ring.
- Catenary_ring wikiPageWikiLink Commutative_ring.
- Catenary_ring wikiPageWikiLink Dedekind_domain.
- Catenary_ring wikiPageWikiLink Dimension_of_an_algebraic_variety.
- Catenary_ring wikiPageWikiLink Excellent_ring.
- Catenary_ring wikiPageWikiLink Local_ring.
- Catenary_ring wikiPageWikiLink Localization_of_a_ring.
- Catenary_ring wikiPageWikiLink Mathematics.
- Catenary_ring wikiPageWikiLink Noetherian_ring.
- Catenary_ring wikiPageWikiLink Prime_ideal.
- Catenary_ring wikiPageWikiLink Quasi-excellent_ring.
- Catenary_ring wikiPageWikiLink Regular_local_ring.
- Catenary_ring wikiPageWikiLink Residue_field.
- Catenary_ring wikiPageWikiLinkText "Catenary ring".
- Catenary_ring wikiPageWikiLinkText "Nagata's example".
- Catenary_ring wikiPageWikiLinkText "catenary property".
- Catenary_ring wikiPageWikiLinkText "catenary ring".
- Catenary_ring wikiPageWikiLinkText "catenary".
- Catenary_ring authorlink "Masayoshi Nagata".
- Catenary_ring first "Masayoshi".
- Catenary_ring hasPhotoCollection Catenary_ring.
- Catenary_ring last "Nagata".
- Catenary_ring loc "page 203 example 2".
- Catenary_ring wikiPageUsesTemplate Template:Citation.
- Catenary_ring wikiPageUsesTemplate Template:Commutative_local_ring_classes.
- Catenary_ring wikiPageUsesTemplate Template:Harvs.
- Catenary_ring wikiPageUsesTemplate Template:Reflist.
- Catenary_ring year "1956".
- Catenary_ring year "1962".
- Catenary_ring subject Category:Algebraic_geometry.
- Catenary_ring subject Category:Commutative_algebra.
- Catenary_ring comment "In mathematics, a commutative ring R is catenary if for any pair of prime ideals p, q,any two strictly increasing chains p=p0 ⊂p1 ... ⊂pn= q of prime idealsare contained in maximal strictly increasing chains from p to q of the same (finite) length.".
- Catenary_ring label "Catenary ring".
- Catenary_ring sameAs Kettenring.
- Catenary_ring sameAs m.02p_hs_.
- Catenary_ring sameAs Q5051871.
- Catenary_ring sameAs Q5051871.
- Catenary_ring sameAs 鏈環.
- Catenary_ring wasDerivedFrom Catenary_ring?oldid=662446494.
- Catenary_ring isPrimaryTopicOf Catenary_ring.