View source for Lasker ring

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A [[Commutative ring|commutative ring]] in which any [[Ideal|ideal]] has a [[Primary decomposition|primary decomposition]], that is, can be represented as the intersection of finitely-many primary ideals. Similarly, an $A$-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 [[#References|[1]]] proved that there is a primary decomposition in polynomial rings. E. Noether [[#References|[2]]] established that any [[Noetherian ring|Noetherian ring]] is a Lasker ring.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  E. Lasker,   "Zur Theorie der Moduln und Ideale"  ''Math. Ann.'' , '''60'''  (1905)  pp. 19–116</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  E. Noether,   "Idealtheorie in Ringbereiche"  ''Math. Ann.'' , '''83'''  (1921)  pp. 24–66</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  N. Bourbaki,   "Elements of mathematics. Commutative algebra" , Addison-Wesley  (1972)  (Translated from French)</TD></TR></table>