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Words: 2k
Articles: 76
Table of contents
2k
76
Frobenius endomorphism
Galois theory
33
Formal derivative in positive characteristic
Galois theory
53
1
Polynomial with zero formal derivative in characteristic p
Formal derivative in positive characteristic
29
Separable polynomial
Galois theory
26
Automorphism-count divisibility theorem
Galois theory
31
Coprime-degree descent for powers
Galois theory
37
Algebraic element
Galois theory
57
1
Minimal polynomial of an algebraic element
Algebraic element
35
Primitive element of a field extension
Galois theory
17
Primitive element theorem
Galois theory
16
Finite separable simple extension implications
Galois theory
46
Biquadratic extension
Galois theory
42
Transitive subgroups of the symmetric group on four points
Galois theory
20
Dihedral Galois action on four radical roots
Galois theory
32
Field embedding
Galois theory
122
3
Linear independence of distinct field embeddings
Field embedding
67
1
Lagrange resolvent eigenvector for a cyclic field automorphism
Linear independence of distinct field embeddings
38
Extension count for field embeddings
Field embedding
34
Tower law for field extensions
Galois theory
12
Splitting field
Galois theory
250
4
Existence and uniqueness of splitting fields
Splitting field
65
Splitting field of x cubed minus two
Splitting field
30
Finite normal extension as a splitting field
Splitting field
61
Splitting field of a polynomial obtained by Frobenius substitution
Splitting field
69
Normal field extension
Galois theory
36
Separable field extension
Galois theory
51
1
Separable algebraic element
Separable field extension
36
Purely inseparable field extension
Galois theory
144
3
Purely inseparable algebraic element
Purely inseparable field extension
72
1
Minimal polynomial of a purely inseparable element
Purely inseparable algebraic element
56
Unique embedding extension through a purely inseparable extension
Purely inseparable field extension
50
Finite Galois extension
Galois theory
42
1
Normal and separable implies Galois
Finite Galois extension
28
Roots of unity in a finite field
Galois theory
32
Kummer extension of rational function fields
Galois theory
33
Galois group of a polynomial
Galois theory
75
1
Transitivity lifted through unique pth roots
Galois group of a polynomial
53
Irreducible factors after Frobenius substitution
Galois theory
119
1
Reducibility criterion after Frobenius substitution
Irreducible factors after Frobenius substitution
69
Frobenius cycle type
Galois theory
25
Dedekind factorization cycle test
Galois theory
27
Cyclotomic polynomial
Galois theory
385
12
Cyclotomic factorization
Cyclotomic polynomial
24
Separability of a cyclotomic polynomial modulo p
Cyclotomic polynomial
33
Galois embedding for a cyclotomic polynomial
Cyclotomic polynomial
38
Cyclotomic field
Cyclotomic polynomial
263
8
Roots of unity in a rational cyclotomic field
Cyclotomic field
20
Seventh cyclotomic field
Cyclotomic field
80
2
Quadratic Gaussian period in the seventh cyclotomic field
Seventh cyclotomic field
22
Real cubic subfield of the seventh cyclotomic field
Seventh cyclotomic field
24
Maximal cyclotomic extension
Cyclotomic field
113
3
Maximal cyclotomic extension of the real numbers
Maximal cyclotomic extension
22
Maximal cyclotomic extension of the rational numbers
Maximal cyclotomic extension
33
Maximal cyclotomic extension of a finite field
Maximal cyclotomic extension
33
Constructible field extension
Galois theory
77
1
Constructibility of the real seventeenth cyclotomic field
Constructible field extension
38
Fixed field
Galois theory
32
Artin fixed-field theorem
Galois theory
28
Galois correspondence
Galois theory
253
5
Normal subextension criterion
Galois correspondence
27
Subextensions of an abelian Galois extension
Galois correspondence
133
2
Cyclic Galois extension of the rational numbers of every finite degree
Subextensions of an abelian Galois extension
39
Finite extensions of the fixed field of a finite-order automorphism of an algebraically closed field
Subextensions of an abelian Galois extension
69
Subfields of the splitting field of x to the fourth minus seven
Galois correspondence
73
Polynomial discriminant
Galois theory
95
3
Vandermonde determinant
Polynomial discriminant
20
Discriminant of a depressed cubic
Polynomial discriminant
8
Discriminant criterion for an alternating Galois group
Polynomial discriminant
48
Lagrange resolvent for a cubic
Galois theory
54
2
Cubic resolvent
Lagrange resolvent for a cubic
30
1
Cardano formula
Cubic resolvent
19
Solvability by radicals
Galois theory
24
Galois group of an irreducible cubic
Galois theory
77
2
Splitting field of x cubed minus x minus one
Galois group of an irreducible cubic
37
Cubic discriminant criterion
Galois group of an irreducible cubic
16
Characteristic-two cubic resolvent
Galois theory
54
Ancestors
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Algebra
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