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: for a cyclic extension L/K of global fields, an element of K is a global norm from L if and only if it is a local norm at every place of K | Statement: [Hasse norm theorem, states, for a cyclic extension L/K of global fields, an element of K is a global norm from L if and only if it is a local norm at every place of K]

Target entity: for a cyclic extension L/K of global fields, an element of K is a global norm from L if and only if it is a local norm at every place of K
Context triple: [Hasse norm theorem, states, for a cyclic extension L/K of global fields, an element of K is a global norm from L if and only if it is a local norm at every place of K]

• A. Hasse norm theorem chosen
  The Hasse norm theorem is a fundamental result in algebraic number theory that characterizes when an element of a global field is a norm from a cyclic extension by relating this property to its behavior in all completions of the field.
• B. Kronecker–Weber theorem
  The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
• C. Artin reciprocity law
  The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
• D. Frobenius element
  The Frobenius element is a distinguished element in a Galois group associated to an unramified prime, encoding how that prime splits in a field extension and playing a central role in algebraic number theory and arithmetic geometry.
• E. Furtwängler’s theorem in class field theory
  Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.