Robert Garbary, Department of Pure Mathematics, University of Waterloo
Nakayama's lemma abstract
The (short-term) goal is to prove that a projective module over a local ring is in fact free. En route to this is a result that pops up enough to have its own name: Nakayama’s Lemma. It is a generalization of the theorem from matrices that a matrix is always a zero of its own characteristic equation. It is proved using a cool trick that is commonly called the ’determinant trick’, which I will talk about.