Triple
T10829476
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Introduction to Commutative Algebra |
E255578
|
entity |
| Predicate | hasSubject |
P450
|
FINISHED |
| Object | Dedekind domains |
E621104
|
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: Dedekind domains | Statement: [Introduction to Commutative Algebra, hasSubject, Dedekind domains]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dedekind domains Context triple: [Introduction to Commutative Algebra, hasSubject, Dedekind domains]
-
A.
Dedekind domain
chosen
A Dedekind domain is an integral domain in which every nonzero proper ideal factors uniquely into a product of prime ideals, playing a central role in algebraic number theory and the study of rings of integers in number fields.
-
B.
Dedekind ideal
A Dedekind ideal is a type of ideal in ring theory central to algebraic number theory, particularly in the study of Dedekind domains and unique factorization of ideals.
-
C.
Noetherian rings
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.
-
D.
Euclidean domains
Euclidean domains are a class of integral domains that admit a division algorithm based on a Euclidean function, generalizing the arithmetic of the integers and enabling efficient computation of greatest common divisors.
-
E.
Krull’s principal ideal theorem
Krull’s principal ideal theorem is a fundamental result in commutative algebra that relates the height of prime ideals containing a principal ideal to the Krull dimension of the ring.
- 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.