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: Galois theory | Statement: [Emil Artin, fieldOfWork, Galois theory]

Target entity: Galois theory
Context triple: [Emil Artin, fieldOfWork, Galois theory]

• A. Galois theory chosen
  Galois theory is a branch of abstract algebra that studies field extensions and polynomial equations through the structure of their associated symmetry groups.
• B. Galois group
  A Galois group is the group of field automorphisms of a field extension that captures the symmetries of its algebraic equations and underpins much of modern algebra and number theory.
• C. Kummer theory
  Kummer theory is a branch of algebraic number theory that studies abelian extensions of fields, especially cyclotomic and radical extensions, using properties of roots of unity and ideal class groups.
• 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. Abel–Ruffini theorem
  The Abel–Ruffini theorem is a fundamental result in algebra proving that there is no general solution in radicals for polynomial equations of degree five or higher.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.