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: Wedderburn’s structure theorem for semisimple rings | Statement: [Artin–Wedderburn theorem, hasComponentResult, Wedderburn’s structure theorem for semisimple rings]

Target entity: Wedderburn’s structure theorem for semisimple rings
Context triple: [Artin–Wedderburn theorem, hasComponentResult, Wedderburn’s structure theorem for semisimple rings]

• A. Artin–Wedderburn theorem chosen
  The Artin–Wedderburn theorem is a fundamental result in ring theory that classifies all semisimple rings as finite direct products of matrix rings over division rings.
• 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. Krull’s principal ideal theorem
  Krull’s principal ideal theorem is a fundamental result in commutative algebra that relates the height of prime ideals containing a principal ideal to the Krull dimension of the ring.
• D. Noether's isomorphism theorems
  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.
• E. Lasker–Noether theorem on primary decomposition
  The Lasker–Noether theorem on primary decomposition is a fundamental result in commutative algebra stating that every ideal in a Noetherian ring can be expressed as a finite intersection of primary ideals, generalizing the factorization of integers into prime powers.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasComponentResult
Context triple: [Artin–Wedderburn theorem, hasComponentResult, Wedderburn’s structure theorem for semisimple rings]

• A. hasComponentWork
  Indicates that one work includes another work as a constituent or subordinate component within it.
• B. hasMainResult chosen
  Indicates that one entity is the primary or most significant outcome, conclusion, or result produced by another entity or process.
• C. hasComponentCurrent
  Indicates that an entity currently includes or contains a specific component as part of its present composition or structure.
• D. hasComponentTest
  Indicates that an entity includes or is associated with a specific test as one of its components.
• E. hasComponentModel
  Indicates that an entity includes or is associated with a specific component model as part of its structure or configuration.
• F. None of above.