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Math! :)


Mar
21
comment Let K/F be a finite extension, given a polynomial in K[x] find another so that their product is in F[x]
This is exactly why I had put the ring theory tag on there as well. My course begins with rings and it seemed as though this problem could be solved using those methods, and here we have it. Thanks Darij!
Mar
18
revised Let K/F be a finite extension, given a polynomial in K[x] find another so that their product is in F[x]
edited title
Mar
18
awarded  Editor
Mar
18
revised Finding the irreducible subrepresentations.
added 167 characters in body
Mar
18
comment Finding the irreducible subrepresentations.
Do you understand what the question (the first paragraph) is asking (it's verbatim from my prof)? I can't seem to parse it into a question that makes sense.
Mar
18
asked Finding the irreducible subrepresentations.
Mar
17
awarded  Supporter
Mar
17
comment Let K/F be a finite extension, given a polynomial in K[x] find another so that their product is in F[x]
let us continue this discussion in chat
Mar
17
comment How to prove $\int_0^a f(x)\,dx=\int_0^a f(a-x)\,dx$
Apply this change to the integral on the right. You'll see that the change brought by the limits of integration and changing from dx to -du cancel out giving you the integral on the left with u instead of x.
Mar
17
awarded  Teacher
Mar
17
answered How to prove $\int_0^a f(x)\,dx=\int_0^a f(a-x)\,dx$
Mar
17
comment Let K/F be a finite extension, given a polynomial in K[x] find another so that their product is in F[x]
@KCd Yes it is. I updated the tags.
Mar
17
revised Let K/F be a finite extension, given a polynomial in K[x] find another so that their product is in F[x]
edited tags
Mar
17
comment What is the maximum number of additive inverse can a number have?
Like Austin said, you probably should specify what axioms we are working under. Usually associativity and commutativity come with the term "additive"
Mar
17
answered What is the maximum number of additive inverse can a number have?
Mar
17
awarded  Student
Mar
17
comment Let K/F be a finite extension, given a polynomial in K[x] find another so that their product is in F[x]
I apologize for coming off mean, I am incredibly grateful. I just wanted to ensure that I understood your proof. Sorry!
Mar
17
comment Let K/F be a finite extension, given a polynomial in K[x] find another so that their product is in F[x]
I think the place where you used the Galois property was in knowing that $w(x)$ is in $F[x]$ because it is fixed by group, this is not something that is true in general for galois groups of non-Galois extensions, right?
Mar
17
comment Let K/F be a finite extension, given a polynomial in K[x] find another so that their product is in F[x]
Awesome. So in the case where the extension is finite but not Galois, I don't want to just consider some Galois extension G/F that has K as an intermediate field and proceed by the same method because then I would not be guaranteed that $w(x)/f(x)$ is in $K[x]$. Also, I don't think you need the assumption that the extension is Galois to know there are only finitely many automorphisms of K that fix F. This comes just from knowing that K/F is a finite extension and it must be contained in some larger extension that is Galois.
Mar
17
comment Let K/F be a finite extension, given a polynomial in K[x] find another so that their product is in F[x]
Hello Patrick, Thanks so much for the help. Just to make sure when you say $\sigma(f(x))$ does this act like $\sigma(a_nx^n \ldots a_1x+a_0)=\sigma(a_n)x^n \ldots \sigma(a_1)x+\sigma(a_0)$?