Commutative algebra 44 Flat modules
Channel: Richard E Borcherds
Date: 2020-10-19

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 summarize some of the properties of flat modules. In particular we show that for finitely presented modules over local rings, free, flat and projective modules are the same. A consequence of this is that for finitely presented modules over any ring, flat and projective modules are the same, and are the analogs of finite rank vector bundles in geometry.

Reading: Section
Exercises: