Algebra learning seminar

Julian Rosen, Department of Pure Mathematics, University of Waterloo

“Projective modules, continued”

Last time, projective modules were introduced. We proved that free modules are projective, and conversely a projective module is always a direct summand of a free module. This time we will prove another connection between free and projective modules: over a commutative ring, a finitely-generated module is projective if and only if it is ”locally free”. One more cool fact: a projective module over a local ring is free (even for noncommutative). See you there!

Please note time change.