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: graded Noether normalization | Statement: [Noether normalization lemma, hasVariant, graded Noether normalization]

Target entity: graded Noether normalization
Context triple: [Noether normalization lemma, hasVariant, graded Noether normalization]

• A. Noether normalization lemma chosen
  The Noether normalization lemma is a fundamental result in commutative algebra and algebraic geometry that shows any finitely generated algebra over a field can be made integral over a polynomial subring, providing a way to relate complicated varieties to affine space.
• B. 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.
• C. Hilbert basis theorem
  The Hilbert basis theorem is a fundamental result in commutative algebra stating that if a ring is Noetherian then any polynomial ring over it is also Noetherian, ensuring that ideals in such rings are finitely generated.
• D. Hilbert’s Nullstellensatz
  Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
• E. Noetherian induction
  Noetherian induction is a proof technique used in mathematics to establish statements about structures satisfying the descending chain condition, generalizing ordinary mathematical induction.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.