Triple
T6833845
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Artinian module |
E157400
|
entity |
| Predicate | overArtinianRing |
P73431
|
FINISHED |
| Object | every finitely generated module is Artinian if and only if it is Noetherian |
—
|
LITERAL FINISHED |
How this triple was built (2 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: every finitely generated module is Artinian if and only if it is Noetherian | Statement: [Artinian module, overArtinianRing, every finitely generated module is Artinian if and only if it is Noetherian]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: overArtinianRing Context triple: [Artinian module, overArtinianRing, every finitely generated module is Artinian if and only if it is Noetherian]
-
A.
isNoetherianRing
Indicates that the ring satisfies the ascending chain condition on ideals, equivalently that every ideal is finitely generated.
-
B.
isRingTheoreticAnalogueOf
Indicates that one concept in ring theory serves as the structural or conceptual counterpart of another notion from a different mathematical context.
-
C.
isIntegrallyClosed
Indicates that a ring (or similar algebraic structure) contains all elements of its field of fractions that are integral over it, i.e., it has no proper integral extension within its field of fractions.
-
D.
hasKrullDimension
Indicates that a mathematical structure (typically a ring or scheme) is associated with a specific Krull dimension, measuring the maximal length of chains of its prime ideals.
-
E.
isDedekindDomain
Indicates that a ring is a Dedekind domain, meaning it is a Noetherian, integrally closed integral domain of Krull dimension one in which every nonzero ideal factors uniquely into prime ideals.
- F. None of above. chosen
Provenance (4 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69c6882c53608190b99aebef079b23bd |
completed | March 27, 2026, 1:37 p.m. |
| NER | Named-entity recognition | batch_69c6d67936288190829fedc3729aadd8 |
completed | March 27, 2026, 7:11 p.m. |
| PD | Predicate disambiguation | batch_69c6d09f90648190bc0a462c7d59de1b |
completed | March 27, 2026, 6:46 p.m. |
| PDg | Predicate description generation | batch_69c6d623aba88190a93ec9c83508c960 |
completed | March 27, 2026, 7:10 p.m. |
Created at: March 27, 2026, 2:18 p.m.