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: Artin–Schreier polynomials | Statement: [Artin–Schreier theory, involves, Artin–Schreier polynomials]

Target entity: Artin–Schreier polynomials
Context triple: [Artin–Schreier theory, involves, Artin–Schreier polynomials]

• A. Artin–Schreier theory
  Artin–Schreier theory is a branch of algebraic number theory and field theory that characterizes cyclic extensions of prime degree in fields of characteristic p using additive polynomials.
• B. Hilbert’s irreducibility theorem
  Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
• C. 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.
• D. Carlitz polynomials
  Carlitz polynomials are a family of polynomials in the theory of function fields over finite fields that serve as analogues of classical Bernoulli polynomials and play a key role in Carlitz module and Drinfeld module theory.
• 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. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Artin–Schreier polynomials
Target entity description: Artin–Schreier polynomials are special polynomials of the form \(x^p - x - a\) over fields of characteristic \(p>0\) that classify certain cyclic extensions of degree \(p\) in Artin–Schreier theory.

• A. Artin–Schreier theory chosen
  Artin–Schreier theory is a branch of algebraic number theory and field theory that characterizes cyclic extensions of prime degree in fields of characteristic p using additive polynomials.
• B. Hilbert’s irreducibility theorem
  Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
• C. 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.
• D. Carlitz polynomials
  Carlitz polynomials are a family of polynomials in the theory of function fields over finite fields that serve as analogues of classical Bernoulli polynomials and play a key role in Carlitz module and Drinfeld module theory.
• 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.