Triple
T21783632
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Artin–Wedderburn theorem |
E537779
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object | Jacobson radical |
—
|
NE NERFINISHED |
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: Jacobson radical | Statement: [Artin–Wedderburn theorem, usesConcept, Jacobson radical]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Jacobson radical Context triple: [Artin–Wedderburn theorem, usesConcept, Jacobson radical]
-
A.
Jacobson radical
chosen
The Jacobson radical is an ideal of a ring that captures elements annihilating all simple modules, playing a key role in understanding the ring’s structure and its representations.
-
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.
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.
-
E.
Dixmier ideal
A Dixmier ideal is a specific type of two-sided ideal in a C*-algebra that plays a key role in the structure and representation theory of operator algebras.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69e0c47198f881908cb0d237266c10e9 |
completed | April 16, 2026, 11:13 a.m. |
| NER | Named-entity recognition | batch_69f046303d54819096b3fab4ab5678e6 |
completed | April 28, 2026, 5:31 a.m. |
Created at: April 16, 2026, 6:52 p.m.