Let be a finitely generatedmodule over a commutativeNoetherian ring. Then there exists a finite set of submodules of such that

1. and is not contained in for all.

2. Each quotient is primary for some prime.

3. The are all distinct for.

4. Uniqueness of the primary component is equivalent to the statement that does not contain for any.

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Cite this as:

Weisstein, Eric W. "Noether-Lasker Theorem."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/Noether-LaskerTheorem.html

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