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Results tagged with galois-theory
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user 2757
Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.
18
votes
Accepted
Disjoint images of polynomials
I guess you won't be satisfied with the answer $f=0$ and $g=1$. :)
But the answer is yes even if you assume that $f$ and $g$ are nonconstant. For example, consider $f(x)=2x^3$ and $g(x)=(x^3-2)^3$. …
- 23.8k
12
votes
Accepted
How to show the galois group of a polynomial is not an alternating group?
There is a version of the Chebotarev density theorem for finitely generated fields, or more precisely, after spreading out, for an étale Galois cover of schemes of finite type over a ring of $S$-integ …
- 23.8k
6
votes
Accepted
Explicit expression of an alternating polynomial in characteristic $2$?
(Here is a more detailed version of Felipe's answer.)
In 1976 Elwyn Berlekamp defined characteristic 2 analogues of the discriminant and its square root, related to the expressions you wrote down. L …
- 23.8k