Triple
T26163376
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Arf rings |
E654173
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | class of commutative rings |
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: class of commutative rings Context triple: [Arf rings, instanceOf, class of commutative rings]
-
A.
result in ring theory
A result in ring theory is a proven mathematical statement that describes properties, structures, or relationships involving rings and their associated algebraic objects.
-
B.
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.
-
C.
noncommutative ring
A noncommutative ring is an algebraic structure consisting of a set equipped with two binary operations, addition and multiplication, where addition forms an abelian group, multiplication is associative and distributes over addition, but multiplication need not be commutative.
-
D.
ring-theoretic structure
A ring-theoretic structure is an algebraic system consisting of a set equipped with two binary operations, typically addition and multiplication, that satisfy the ring axioms such as associativity, distributivity, and the existence of an additive identity and inverses.
-
E.
Noetherian ring
A Noetherian ring is a ring in which every ascending chain of ideals stabilizes, equivalently, every ideal is finitely generated.
- 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_69ee5b44391c81908bdbd8813ba9aa99 |
completed | April 26, 2026, 6:36 p.m. |
Created at: April 26, 2026, 8:31 p.m.