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: Auslander–Buchsbaum theorem | Statement: [Auslander–Buchsbaum formula, relatedTo, Auslander–Buchsbaum theorem]

Target entity: Auslander–Buchsbaum theorem
Context triple: [Auslander–Buchsbaum formula, relatedTo, Auslander–Buchsbaum theorem]

• A. Auslander–Buchsbaum formula chosen
  The Auslander–Buchsbaum formula is a fundamental result in commutative algebra that relates the projective dimension of a finitely generated module over a Noetherian local ring to the depth of the module and the depth of the ring.
• B. Hilbert’s syzygy theorem
  Hilbert’s syzygy theorem is a fundamental result in commutative algebra that describes the finite length and structure of free resolutions of modules over polynomial rings.
• C. Krull–Gabriel dimension
  Krull–Gabriel dimension is a refinement of Krull dimension used in the representation theory of rings and abelian categories to measure the complexity of their subobject lattices and module categories.
• D. 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.
• E. Castelnuovo–Mumford regularity
  Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.