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

In Branch

Commutative Algebra

Source Primary decomposition (Wikipedia)

Proved By

Emanuel Lasker

Source Primary decomposition (Wikipedia)

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)

View the Source

Primary decomposition (Wikipedia)

Proved By: Emanuel Lasker, Lead sentence, attribution
first proven by Emanuel Lasker (1905)
In Group: Ring Theory and Commutative Algebra, Lead section
mathematics, the Lasker-Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal
In Branch: Commutative Algebra, Lead section
mathematics, the Lasker-Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed

Switch Atlas

The Inner World

The Civil World

The Natural World

Lasker-Noether Theorem

Has Statement Form

In Branch

Proved By