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Excellent ring

In commutative algebra, a quasi-excellent ring is a Noetherian commutative ring that behaves well with respect to the operation of completion, and is called an excellent ring if it is also universally catenary. Excellent rings are one answer to the problem of finding a natural class of "well-behaved" rings containing most of the rings that occur in…

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Resolution of singularities

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Excellent ring

Nodes54
Edges53
Triples59
Avg. degree1.96
Density0.037037
Components1

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Excellent ring

Top relations

related to References · 30
Excellent ring → Alexandre Grothendieck, Algebraic Variety Over, Annals, Benjamin/Cummings Pub, Chapter, Characteristic Zero, Co, Commutative, Danilov, Eléments, EMS PressHironaka, Encyclopedia, Excellent, Field, Heisuke, Hideyuki, Hironaka, IHÉS, II, ISBN
related to Excellent rings · 10
Excellent ring → All, All Dedekind, Any, Dedekind, In, Most, Noetherian, The, This, Zp
related to Resolution of singularities · 6
Excellent ring → Conversely, Grothendieck, Grothendieck's, Hironaka, Noetherian, Quasi-excellent
related to Properties · 5
Excellent ring → Because, G-ring, In, Noetherian, This
related to Definitions · 4
Excellent ring → Although, Dedekind, Noetherian, The
is a · 2
Excellent ring → Nagata ring.Any quasi-excellent reduced local ring is analytically reduced.Any quasi-excellent normal local ring is analytically normal, Noetherian commutative ring that behaves well with respect to the operation of completion
related to Quasi-excellence · 2
Excellent ring → Any, Nagata

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Important terminology

ring excellent rings noetherian quasi-excellent g-ring local characteristic singularities j-2 displaystyle called catenary algebraic regular universally problem resolution field finite

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Excellent ringis aNoetherian commutative ring that behaves well with respect to the operation of completion0.90text
Excellent ringis aNagata ring.Any quasi-excellent reduced local ring is analytically reduced.Any quasi-excellent normal local ring is analytically normal0.90text
Excellent ringrelated to DefinitionsThe0.60section
Excellent ringrelated to DefinitionsAlthough0.60section
Excellent ringrelated to DefinitionsNoetherian0.60section
Excellent ringrelated to DefinitionsDedekind0.60section
Excellent ringrelated to Excellent ringsMost0.60section
Excellent ringrelated to Excellent ringsIn0.60section
Excellent ringrelated to Excellent ringsAll0.60section
Excellent ringrelated to Excellent ringsNoetherian0.60section
Excellent ringrelated to Excellent ringsZp0.60section
Excellent ringrelated to Excellent ringsAll Dedekind0.60section

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