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Nov19-07, 06:27 PM
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Quote Quote by pivoxa15 View Post
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,...p-1 with multiplication mod p can be used to show for all m, m^p-1=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