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Nov17-07, 04:07 PM
P: 2,268
Quote Quote by Kummer View Post
No. Field theory in particular over finite fields and rational numbers. And Galois theory are used a lot in number theory. That is probably the largest area of algebra that is used in number theory. And p-adic analysis.
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.