Artinian module
E157400
An Artinian module is an algebraic structure over a ring that satisfies the descending chain condition on its submodules, meaning every decreasing sequence of submodules eventually stabilizes.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Artinian module canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1382843 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Artinian module Context triple: [Noetherian module, contrastsWith, Artinian module]
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A.
Artime
Artime is a Spanish-language surname of likely Iberian origin borne by various individuals, including figures in Latin American history and culture.
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B.
Mathnawi
Mathnawi is a monumental six-volume Persian Sufi poetic work by Rumi that explores mystical love, spiritual wisdom, and the path to divine union.
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C.
AMM
AMM is the commonly used abbreviation for the APEC Ministerial Meeting, the annual gathering of Asia-Pacific Economic Cooperation foreign and trade ministers.
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D.
Almus
Almus is a figure in Greek mythology known as a son of Merope and associated with the region of Orchomenus in Boeotia.
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E.
ARITC
ARITC is a British Army organization responsible for overseeing recruitment and the initial training of new soldiers.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Artinian module Target entity description: An Artinian module is an algebraic structure over a ring that satisfies the descending chain condition on its submodules, meaning every decreasing sequence of submodules eventually stabilizes.
-
A.
Artime
Artime is a Spanish-language surname of likely Iberian origin borne by various individuals, including figures in Latin American history and culture.
-
B.
Mathnawi
Mathnawi is a monumental six-volume Persian Sufi poetic work by Rumi that explores mystical love, spiritual wisdom, and the path to divine union.
-
C.
AMM
AMM is the commonly used abbreviation for the APEC Ministerial Meeting, the annual gathering of Asia-Pacific Economic Cooperation foreign and trade ministers.
-
D.
Almus
Almus is a figure in Greek mythology known as a son of Merope and associated with the region of Orchomenus in Boeotia.
-
E.
ARITC
ARITC is a British Army organization responsible for overseeing recruitment and the initial training of new soldiers.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic structure
ⓘ
mathematical object ⓘ module theory concept ⓘ |
| abbreviation | Artinian R-module ⓘ |
| appearsIn |
Wedderburn–Artin theory
ⓘ
linked to:
Artin–Wedderburn theorem
|
| characterizedBy | finite length over semiprimary rings ⓘ |
| closedUnder |
finite direct sums
ⓘ
quotient modules ⓘ submodules ⓘ |
| context |
abstract algebra
ⓘ
module theory ⓘ |
| contrastedWith | Noetherian module defined by ascending chain condition ⓘ |
| definedOver | ring ⓘ |
| dualTo | Noetherian module ⓘ |
| generalizes | Artinian ring ⓘ |
| hasChainCondition | descending chain condition on submodules ⓘ |
| hasCondition | every descending chain of submodules stabilizes ⓘ |
| hasDecomposition | composition series when of finite length ⓘ |
| hasEquivalentDefinition | every nonempty set of submodules has a minimal element ⓘ |
| hasExample |
finite abelian groups as Z-modules
ⓘ
finite length modules ⓘ modules over Artinian rings that are finitely generated ⓘ |
| hasProperty |
every Artinian module has finite length over a semiprimary ring
ⓘ
every nonzero Artinian module has a simple submodule ⓘ intersection of all maximal submodules can be nonzero ⓘ satisfies descending chain condition on submodules ⓘ |
| implies |
Jacobson radical acts nilpotently on some classes of modules
ⓘ
module has minimal submodules ⓘ module is of finite length over a left Artinian ring ⓘ |
| isGeneralizationOf | Artinian abelian group ⓘ |
| namedAfter | Emil Artin ⓘ |
| notEquivalentTo | Noetherian module in general ⓘ |
| overArtinianRing |
every finitely generated module is Artinian if and only if it is Noetherian
ⓘ
every module of finite length is Artinian ⓘ |
| relatedConcept |
Artinian ring
ⓘ
Noetherian module ⓘ finite length module ⓘ semisimple module ⓘ |
| studiedIn | homological algebra ⓘ |
| usedIn |
noncommutative ring theory
ⓘ
representation theory of algebras ⓘ structure theory of modules ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Artinian module Description of subject: An Artinian module is an algebraic structure over a ring that satisfies the descending chain condition on its submodules, meaning every decreasing sequence of submodules eventually stabilizes.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.