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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.
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
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
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