The previous lecture in this series is here. The next lecture in this series is here.
We mainly discuss the problem of whether free modules over a ring have a well defined rank, generalizing the dimension of a vector space. We show that they do over many rings, including all non-zero commutative rings, but give an example of a non-commutative ring where the rank of a free module is not defined.
This video is part of a lecture course by Richard Borcherds from 2021.