Quote by Kummer
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 padic 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.