Splitting Fields; Multiple Roots Flashcards
1
Q
Generalization of this proposition
A
2
Q
Splitting field, example
A
3
Q
Degree of a splitting field, remark and examples
A
4
Q
F-homomorphisms and field generated by roots of f; corollary
A
5
Q
Remarks about corollary
A
6
Q
Proposition about GCDs
A
7
Q
Multiple roots; example
A
8
Q
Proposition about multiple roots and the derivative
A
9
Q
Separable definition
A
10
Q
Perfect fields
A
11
Q
Examples of perfect fields
A
12
Q
F-automorphisms; examples
A
13
Q
Examples
A
14
Q
Corollary
A
15
Q
Separable, Normal; example
A
16
Q
Galois; defintion and theorem
A
17
Q
Conjugates; remark and corollary
A
18
Q
separable degree; remark
A
19
Q
Fundamental Theorem of Galois Theory
A
20
Q
A
21
Q
A
22
Q
Galois group of a polynomial
A
23
Q
Solvability in radicals
A
24
Q
failure of solvability of radicals theorem for char p
A
