i'm doing all this megarigorous commutative algebra in a class and i want to see what it's building up to, but i don't just want to read hartshorne/a megarigorous algebraic geometry textbook, i'm looking for basically the "softest" book on A.G. there is so I can read it concurrently for motivation.
i even liked the bit of analytic number theory that i saw, went through chebyshev's theorem proof in detail for a course project. (which says a lot, i generally can't stand analysis.)
Theory of equation consists of galois theory, solving lower degree equations on $\mathbb{ \bar Q}$ and solving higher degree equations (quintics, sextics, etc) in larger extensions of operations.
maybe what we have here is just a difference in terminology.
in any case, i actually do not have too much interest in galois theory, unfortunately. some of it is interesting, but i am more interested in other areas of algebra.
@BalarkaSen but galois theory addresses how to solve quintics. maybe in my neck of the woods the phrase galois theory is used more broadly than in yours.
@AlexanderGruber Perhaps. But I like to keep it theory of equations, since sometimes much more than that of galois theory is needed to answer some questions.
@DanielFischer: I apologize for not @-pinging on my edit. The whole intention of the thank you was to get your attention, but I accidentally left out the @-ping.
No, that won't work. If you have an element of $C(n)$ and one of $C(m)$, pick some $p$ coprime to both of those. Then they both map to the same element of $C(p)$
So that the direct limit of $C(n)$ will be trivial.
