Theorem

Lasker-Noether Theorem

Algebra

The Lasker-Noether Theorem states that every ideal of a Noetherian ring can be decomposed as an intersection of finitely many primary ideals, a primary decomposition generalizing the factorization of an integer into prime powers. The special case for polynomial rings and convergent power series rings was first proved by Emanuel Lasker, and the theorem was established in its full generality by Emmy Noether.

Facts

Statement

Every ideal of a Noetherian ring can be decomposed as an intersection of finitely many primary ideals, called a primary decomposition. 1

Proof Year

1921 1

Classification

Statement Form

Existence Theorem 1

Connections

Has Statement Form

Existence Theorem

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Sources

1. Lasker-Noether theorem, Wikipedia

Introduction
the Lasker-Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals
Historical attribution
was proven in its full generality by Emmy Noether (1921)

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Lasker-Noether Theorem

Has Statement Form