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Lasker ring

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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.

References

[1] E. Lasker, "Zur Theorie der Moduln und Ideale" Math. Ann. , 60 (1905) pp. 19–116
[2] E. Noether, "Idealtheorie in Ringbereiche" Math. Ann. , 83 (1921) pp. 24–66
[3] N. Bourbaki, "Elements of mathematics. Commutative algebra" , Addison-Wesley (1972) (Translated from French)
How to Cite This Entry:
Lasker ring. V.I. Danilov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Lasker_ring&oldid=15831
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098