Commutative algebra 27 (Associated primes)
Channel: Richard E Borcherds
Date: 2020-08-26

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 show that every finitely generated module M over a Noetherian ring R can broken up into modules of the form R/p for p prime, and give some examples to show that the multiplicity of R/p in M is not additive. We then introduce the set of associated primes of a modules, and show that it is finite. 

Reading: Section 3.1
Exercises: 3.1, 3.2, 3.14