Commutative algebra 58: System of parameters versus Krull
Channel: Richard E Borcherds
Date: 2020-12-13

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 the smallest size of a system of parameters of a Noetherian local ring is at most the Krull dimension. The proof uses the "prime avoidance theorem". Together with the results of the previous two lectures, this shows that the three definitions we gave of the dimension of a Noetherian local ring are all equivalent. 

Reading: Section
Exercises: