Triple
T10829458
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Introduction to Commutative Algebra |
E255578
|
entity |
| Predicate | hasSubject |
P450
|
FINISHED |
| Object | Noetherian rings |
E157398
|
NE 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: Noetherian rings | Statement: [Introduction to Commutative Algebra, hasSubject, Noetherian rings]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Noetherian rings Context triple: [Introduction to Commutative Algebra, hasSubject, Noetherian rings]
-
A.
Noetherian rings
chosen
Noetherian rings are a fundamental class of rings in commutative algebra characterized by the property that every ascending chain of ideals stabilizes, ensuring that all ideals are finitely generated.
-
B.
Cohen–Macaulay ring
A Cohen–Macaulay ring is a commutative Noetherian ring whose depth equals its Krull dimension, giving it especially well-behaved homological and geometric properties.
-
C.
Noetherian induction
Noetherian induction is a proof technique used in mathematics to establish statements about structures satisfying the descending chain condition, generalizing ordinary mathematical induction.
-
D.
Noetherian module
A Noetherian module is an algebraic structure in which every ascending chain of submodules stabilizes, ensuring that all submodules are finitely generated and enabling powerful finiteness arguments in ring and module theory.
-
E.
ring theory
Ring theory is a branch of abstract algebra that studies rings—algebraic structures equipped with two binary operations generalizing addition and multiplication of integers—and their ideals, modules, and homomorphisms.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d6aa8081448190a9324184f2bd1c26 |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d74420fa188190b5b3c59e1a9f551d |
completed | April 9, 2026, 6:16 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69de85a068b08190948c3ca32cdda147 |
completed | April 14, 2026, 6:21 p.m. |
Created at: April 8, 2026, 9:19 p.m.