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: "Commutative Algebra, Volume I" | Statement: [Oscar Zariski, coWrote, "Commutative Algebra, Volume I"]

Target entity: "Commutative Algebra, Volume I"
Context triple: [Oscar Zariski, coWrote, "Commutative Algebra, Volume I"]

• A. Eisenbud’s Commutative Algebra
  Eisenbud’s *Commutative Algebra* is a widely used graduate-level textbook that develops modern commutative algebra with strong connections to algebraic geometry, featuring topics such as free resolutions, syzygies, and Castelnuovo–Mumford regularity.
• B. Cours d’algèbre commutative
  Cours d’algèbre commutative is a foundational French textbook on commutative algebra authored by mathematician Jean-Daniel Perrin.
• C. “Introduction to Commutative Algebra” (with Ian G. Macdonald)
  “Introduction to Commutative Algebra” (with Ian G. Macdonald) is a classic introductory textbook that provides a concise, rigorous foundation in commutative algebra, widely used by advanced undergraduates and beginning graduate students in mathematics.
• 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. Moderne Algebra
  Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: "Commutative Algebra, Volume I"
Target entity description: "Commutative Algebra, Volume I" is a foundational graduate-level textbook in modern algebra that systematically develops the theory of commutative rings and ideals, coauthored by Oscar Zariski.

• A. Eisenbud’s Commutative Algebra
  Eisenbud’s *Commutative Algebra* is a widely used graduate-level textbook that develops modern commutative algebra with strong connections to algebraic geometry, featuring topics such as free resolutions, syzygies, and Castelnuovo–Mumford regularity.
• B. Cours d’algèbre commutative
  Cours d’algèbre commutative is a foundational French textbook on commutative algebra authored by mathematician Jean-Daniel Perrin.
• C. “Introduction to Commutative Algebra” (with Ian G. Macdonald)
  “Introduction to Commutative Algebra” (with Ian G. Macdonald) is a classic introductory textbook that provides a concise, rigorous foundation in commutative algebra, widely used by advanced undergraduates and beginning graduate students in mathematics.
• 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. Moderne Algebra
  Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
• F. None of above. chosen