materials

topics

This week, we’ll talk about the following:

for an ideal \(I\) of a ring \(R\), the quotient group \(R/I\) has the structure of a ring
after that, the goal for the week will be to introduce analogues of basic notions from linear algebra, but where the scalars are taken from an arbitrary commutative ring
the notion of a category, and explain why initial and terminal objects in a category are unique
the notion of a product and a co-product in a category
the notion of a module over a commutative ring
the notion of the direct sum of modules (a co-product in the category of modules).
the notion of a free module, meaning module with a basis.