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Revision as of 17:06, 5 June 2024

invariant of rings and modules in algebra

Language	Label	Description	Also known as
English	depth	invariant of rings and modules in algebra

Statements

subclass of

invariant

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defining formula

${\displaystyle \operatorname {depth} _{I}(M)=\min\{i\colon \operatorname {Ext} ^{i}(R/I,M)\neq 0\}}$

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in defining formula

${\displaystyle \operatorname {depth} }$

symbol represents

depth

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${\displaystyle M}$

symbol represents

finitely generated module

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${\displaystyle R}$

symbol represents

commutative ring

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${\displaystyle I}$

symbol represents

two-sided ideal

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${\displaystyle /}$

symbol represents

quotient ring

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${\displaystyle \operatorname {Ext} }$

symbol represents

Ext functor

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

Encyclopedia of Mathematics article ID

Depth_of_a_module

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Freebase ID

/m/02prpy1

1 reference

stated in

Freebase Data Dumps

publication date

28 October 2013

 

Sitelinks

Wikipedia(10 entries)

• dewiki Tiefe (Kommutative Algebra)
• elwiki Βάθος (θεωρία δακτυλίων)
• enwiki Depth (ring theory)
• fawiki عمق (نظریه حلقه‌ها)
• frwiki Anneau de Cohen-Macaulay
• itwiki Profondità (algebra)
• jawiki 深さ (環論)
• kowiki 가군의 깊이
• ukwiki Глибина (теорія кілець)
• zhwiki 深度 (模論)

Wikibooks(0 entries)

Wikinews(0 entries)

Wikiquote(0 entries)

Wikisource(0 entries)

Wikiversity(0 entries)

Wikivoyage(0 entries)

Wiktionary(0 entries)

Multilingual sites(0 entries)

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