Date and Time
-
Location
MSB Room 12
Organizers
Speaker
Kaustubh Verma

In this talk we will introduce the notion of a Kaplansky devissage and show its key properties. We will use these properties to prove that any projective module is some direct sum of countably generated projective submodules. We then define the direct sum property for modules and show that any countably generated module with the direct sum property is free. We finally show that any projective module over a local ring has the direct sum property letting us conclude that all projective modules over local rings are free.