Commutative algebra 21 Tensor products and exactness
Channel: Richard E Borcherds
Date: 2020-08-22

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.

In this lecture we study when taking tensor product preserves exactness.
We also show that tensor products preserve direct limits, and show how to use this to calculate some examples of tensor products, such as the tensor product of Q and Q.

Reading: Section 2.2
Exercise: 2.13
Calculate Hom(M,N) and the tensor products of M, N over the ring k[x] for all pairs M,N of modules each of which is isomorphic to k(x), k[x], or k[x]/(f^n) where f is an irreducible polynomial.