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: Lasker–Noether theorem on primary decomposition | Statement: [Noetherian ring, hasTheorem, Lasker–Noether theorem on primary decomposition]

Target entity: Lasker–Noether theorem on primary decomposition
Context triple: [Noetherian ring, hasTheorem, Lasker–Noether theorem on primary decomposition]

• A. 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.
• 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. Hilbert’s fourteenth problem
  Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
• D. 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.
• 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. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Lasker–Noether theorem on primary decomposition
Triple: [Noetherian ring, hasTheorem, Lasker–Noether theorem on primary decomposition]

The Lasker–Noether theorem on primary decomposition is a fundamental result in commutative algebra stating that every ideal in a Noetherian ring can be expressed as a finite intersection of primary ideals, generalizing the factorization of integers into prime powers.

Target entity: Lasker–Noether theorem on primary decomposition
Target entity description: The Lasker–Noether theorem on primary decomposition is a fundamental result in commutative algebra stating that every ideal in a Noetherian ring can be expressed as a finite intersection of primary ideals, generalizing the factorization of integers into prime powers.

• A. 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.
• 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. Hilbert’s fourteenth problem
  Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
• D. 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.
• 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. chosen