Difference between revisions of "Equidimensional ring"

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===Stronger properties===
 
===Stronger properties===
  
* [[Local Cohen-Macaulay ring]]
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{| class="sortable" border="1"
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! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
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|-
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| [[Weaker than::local Cohen-Macaulay ring]] || || || || {{intermediate notions short|equidimensional ring|local Cohen-Macaulay ring}}
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|-
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| [[Weaker than::local Noetherian domain]] || [[integral domain]] with a unique [[maximal ideal]] || || || {{intermediate notions short|equidimensional ring|local Noetherian domain}}
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|}

Latest revision as of 04:32, 18 July 2013

This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
View all properties of commutative unital rings
VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions

Definition

A commutative unital ring is said to be equidimensional if it satisfies both the following conditions:

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
local Cohen-Macaulay ring click here
local Noetherian domain integral domain with a unique maximal ideal click here