Galois Theory Intro Cut Short - Seeking Resources

Kindayr
Messages
159
Reaction score
0
I was taking a lecture series this summer at my school where a professor was introducing us to introductory Galois theory. It was a very 'slack' introduction, without too much rigour. However, about a month in (only 3-4, 3 hr lectures) they stopped due to outstanding circumstances.

I was a little upset due to how the course basically got my juices flowing for Galois theory and 'tougher' algebra.

I was wondering if anyone had some online resources, or was even willing to walk me through it here in this thread out of interest.

We had started from basically nothing (it was not expected to have any experience in group, ring or field theory). We had just began to discuss ideals before its abrupt end.

Anything anyone has to offer is awesome, conceptual or rigourous.

Thanks ahead :)
 
Physics news on Phys.org
Whoa, that's exactly what I was looking for, perfect :)


Thanks
 
I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
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...
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...
Back
Top