Commutative algebra 28 Geometry of associated primes
Channel: Richard E Borcherds
Date: 2020-08-28

This lecture is part of an online course on commutative algebra, following the book
"Commutative algebra with a view toward algebraic geometry" by David Eisenbud.

We give a geometric interpretation of Ass(M), the set of associated primes of M, by showing that its closure is the support Supp(M) of the module M in the spectrum Spec(R). We give several examples, such as some Z-modules, and the module R/(y^2, xy) over the ring R=k[x,y]. Finally we give an introduction to the coprimary decomposition of a module, and discuss an earlier form of it called the Lasker-Noether theorem. 

Reading: Section 3.2
Exercises: 3.16, 3.17, 3.20