A commutative ring in which any ideal has a primary decomposition, that is, can be represented as the intersection of finitely-many primary ideals. Similarly, an -module is called a Lasker module if any submodule of it has a primary decomposition. Any module of finite type over a Lasker ring is a Lasker module. E. Lasker [1] proved that there is a primary decomposition in polynomial rings. E. Noether [2] established that any Noetherian ring is a Lasker ring.

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