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: Henselian ring | Statement: [Kurt Hensel, hasEponym, Henselian ring]

Target entity: Henselian ring
Context triple: [Kurt Hensel, hasEponym, Henselian ring]

• A. Henselian ring chosen
  A Henselian ring is a local ring in which Hensel’s lemma holds, allowing certain types of polynomial factorizations and root liftings from the residue field to the ring itself.
• B. Henselization
  Henselization is a construction in commutative algebra that minimally modifies a local ring to satisfy Hensel’s lemma, making it “Henselian” while preserving much of its original structure.
• C. Hensel’s lemma
  Hensel’s lemma is a fundamental result in number theory and p-adic analysis that allows one to lift solutions of polynomial congruences modulo a prime power to higher powers, analogous to Newton’s method in the p-adic setting.
• D. 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.
• E. Hasse–Arf theorem
  The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.