Commutative algebra 49: Completions
Channel: Richard E Borcherds
Date: 12/11/2020

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 define the completion of a ring and give some examples: the ring of formal power series, and the ring of 10-adic integers. 

We discuss the relation between the localization  and completion of rings at a maximal ideal, and show that although the localaization of an integral domain is an integral domain, the completion at a maximal ideal need not be. 

Finally we draw a picture of the 2-adic integers. 

Reading: Section
Exercises: