Rota–Baxter ideal
E1237911
UNEXPLORED
A Rota–Baxter ideal is an ideal in a Rota–Baxter algebra that is stable under the Rota–Baxter operator, making it the natural notion of an ideal compatible with the algebra’s Rota–Baxter structure.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Rota–Baxter ideal canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T16876529 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Rota–Baxter ideal Context triple: [Rota–Baxter algebra, hasConcept, Rota–Baxter ideal]
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A.
Rota–Baxter algebra
A Rota–Baxter algebra is an associative algebra equipped with a linear operator satisfying a specific integration-like identity that generalizes the properties of integral and summation operators in algebraic form.
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B.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
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C.
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.
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D.
Gelfand–Kirillov dimension
The Gelfand–Kirillov dimension is an invariant in noncommutative algebra that measures the growth rate of algebras and modules, serving as an analogue of Krull dimension for noncommutative settings.
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E.
Jordan–Chevalley decomposition
The Jordan–Chevalley decomposition is a fundamental result in linear algebra and representation theory that expresses a linear operator (or matrix) as the sum or product of commuting semisimple and nilpotent parts.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Rota–Baxter ideal Target entity description: A Rota–Baxter ideal is an ideal in a Rota–Baxter algebra that is stable under the Rota–Baxter operator, making it the natural notion of an ideal compatible with the algebra’s Rota–Baxter structure.
-
A.
Rota–Baxter algebra
A Rota–Baxter algebra is an associative algebra equipped with a linear operator satisfying a specific integration-like identity that generalizes the properties of integral and summation operators in algebraic form.
-
B.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
-
C.
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.
-
D.
Gelfand–Kirillov dimension
The Gelfand–Kirillov dimension is an invariant in noncommutative algebra that measures the growth rate of algebras and modules, serving as an analogue of Krull dimension for noncommutative settings.
-
E.
Jordan–Chevalley decomposition
The Jordan–Chevalley decomposition is a fundamental result in linear algebra and representation theory that expresses a linear operator (or matrix) as the sum or product of commuting semisimple and nilpotent parts.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.