Triple
T25073830
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euclidean domain |
E627994
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | commutative ring |
C21322
|
CONCEPT FINISHED |
How this triple was built (1 step)
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.
CD
Concept disambiguation
gpt-5-mini-2025-08-07
Target class: commutative ring Context triple: [Euclidean domain, instanceOf, commutative ring]
-
A.
commutative algebra concept
chosen
A commutative algebra concept is an abstract mathematical notion involving commutative rings, their ideals, modules, and related structures, used to study algebraic properties that often underlie geometry and number theory.
-
B.
Noetherian ring
A Noetherian ring is a ring in which every ascending chain of ideals stabilizes, equivalently, every ideal is finitely generated.
-
C.
principal ideal domain
A principal ideal domain is an integral domain in which every ideal is generated by a single element.
-
D.
ring homomorphism
A ring homomorphism is a function between rings that preserves addition, multiplication, and the multiplicative identity (when present), mapping the structure of one ring compatibly into another.
-
E.
nonassociative ring
A nonassociative ring is an algebraic structure with two binary operations (addition and multiplication) where addition forms an abelian group, multiplication is distributive over addition, but multiplication is not required to be associative.
- F. None of above.
Provenance (1 batch)
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_69e2ff2d71dc8190b4758e57d643cbe4 |
completed | April 18, 2026, 3:49 a.m. |
Created at: April 18, 2026, 6:20 a.m.