Commutative algebra 33 (Integral elements)
Channel: Richard E Borcherds
Date: 2020-09-02

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.

This lecture covers some basic properties of integral elements and finite extensions. We show that an extension is finite if and only if it is generated by a finite number of integral elements (using the Cayley-Hamilton theorem).
We also define the normalization of an integral domain as its integral closure in the field of quotients, and calculate the normalization of Z[sqrt(5)]. 

Reading: Section 4.1, 4.2
Exercises: 4.1, 4.20