Degree of Rational Function Field

jose80
Messages
4
Reaction score
0
Hi,

I am trying to find the degree [F_{q^2}(x):F_{q}(x)]$.

Intuitively, I thought it will be 2? but cannot see that
 
Physics news on Phys.org
What do you mean with that notation?? The index as groups or the index as fields?? If it is the index as groups, then the answer is q. If it is as fields, then the answer is 2.
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

MHB Checking if $\beta \in \text{Isom}(\mathbb{R}^2)$
Replies
15
Views
1K
I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
Replies
48
Views
3K
I Generators of Galois group of ## X^n - \theta ##
Replies
3
Views
2K
B Subspaces of Functions- definition
Replies
8
Views
2K
I Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
Replies
0
Views
2K
I Matrix rank in terms of determinant polynomial
Replies
14
Views
3K
I Make a list of all irreducible polynomials of degrees 1 to 5 over F2
Replies
4
Views
2K
MHB Find the minimal polynomial of some value a over Q
Replies
1
Views
2K
I Rational functions in one indeterminate - useful concept?
Replies
31
Views
5K
I Mean values of observables
Replies
2
Views
937

Hot Threads

Recent Insights

Back
Top