Triple

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).

Phrase: Noether isomorphism theorems | Statement: [Noether's isomorphism theorems, alsoKnownAs, Noether isomorphism theorems]

Target entity: Noether isomorphism theorems
Context triple: [Noether's isomorphism theorems, alsoKnownAs, Noether isomorphism theorems]

• A. Noether's isomorphism theorems chosen
  Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
• B. Jordan–Hölder theorem
  The Jordan–Hölder theorem is a fundamental result in group theory stating that any two composition series of a finite group have the same length and the same (up to order and isomorphism) simple factor groups.
• C. Abelian groups
  Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
• D. Noether's problem
  Noether's problem is a fundamental question in invariant theory and field theory that asks whether the fixed field of a finite group acting on a rational function field is itself a purely transcendental (rational) extension.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.