-1
votes
0answers
27 views

Schanuel's conjecture and field extensions.

Doing a little bit of reading over the summer break before going into my masters year of my maths degree and i have been looking at Schanuel's conjecture which states that; Given any $n$ complex ...
3
votes
1answer
69 views

Question about notation in a theorem about Galois theory from Lang's Algebra (chapter 6 §1, corollary 1.16)

I have a question about the notation in an assertion in Lang's Algebra, chapter 6 §1, corollary 1.16: Let $K/k$ be finite Galois with group $G$, and assume that $G$ can be written as a direct ...
6
votes
1answer
144 views

What does this notation mean: $\displaystyle\lim_{\leftarrow} \,\mathbb{Z}/n\mathbb{Z}$?

Just a small notation question from this Wikipedia page: The absolute Galois group of a finite field $K$ is isomorphic to the group $$\hat{\mathbb{Z}}=\lim_{\leftarrow} \mathbb{Z}/n\mathbb{Z}.$$ ...
4
votes
1answer
237 views

Field extensions, inverse limits, notation and roots of unity

I'm hoping I can get some assistance with a revision problem and also a notational issue I'm not sure about (although it may not be standard). I seem to remember going over this or something similar ...
1
vote
1answer
56 views

Notation question involving discriminant identity

Let $f \in K[X] $ be an irreducible, separable polynomial, and let $M/K$ be a splitting field for $f$. Let $\alpha \in M$ be a root of $f$. Then $D(f) = (-1)^{d(d-1)/2} N_{K/k} (f'(\alpha))$, ...