Quote by pivoxa15
All fields are rings, but not conversely.
You said, '...algebra and number theory are related as soon as you start learning about them...'
I assume one does not learn Galois theory as the first exposure to algebra. One does rings and group theory before moving on to Galois theory which uses a combination of them.

You can do number theory using rings and groups. For example, the group of integers 1,...p1 with multiplication mod p can be used to show for all m, m^p1=1 mod p, a trivial result once you talk about the order of a group. I'm sure there are other things I can't remember off the top of my head