Ring Theory: We consider integral domains, which are commutative rings that contain no zero divisors. We show that this property is equivalent to a cancellation law for the ring. Finally we note some basic connections between integral domains and fields.

You’re welcome!

We’ll need this for field theory. If R is a field, then it must contain a subfield iso to Q or some Z/p. Checking the definitions, R becomes a vector space over this subfield and linear algebra enters the picture.

At this point though, we like to have some familiar objects around when working with arbitrary R. I bring up the subring generated by 1 again in the next video.