Question

Elements of Galois group map roots of minimal polynomial to which other roots?

score 210 · Answer 1 · 2026-04-16 03:12:49

210

Views

Elements of Galois group map roots of minimal polynomial to which other roots?

Published on 16 Apr 2026 - 3:12

score 239 · Answer 2 · 2026-04-12 17:00:02

239

Views

Can inseparable elements “appear” in the residue field of the Galois closure of a field extension with separable residue field extension?

Published on 12 Apr 2026 - 17:00

score 206 · Answer 3 · 2026-04-16 03:32:00

206

Views

Suppose $K$ is a Galois extension of $F$. Consider $E/F$ a finite extension such that $K\cap E=F$. Show that $[KE:K]=[E:F]$.

Published on 16 Apr 2026 - 3:32

score 275 · Answer 4 · 2026-04-14 05:14:37

275

Views

Existence of a Field not containing $\sqrt{2}$, such that any finite extension is cyclic.

Published on 14 Apr 2026 - 5:14

score 94 · Answer 5 · 2026-04-15 14:12:23

94

Views

Galois group for $\operatorname{Gal}(\mathbb{Q}(\zeta_n + \zeta_n^{-1})/\mathbb{Q})$

Published on 15 Apr 2026 - 14:12

score 43 · Answer 6 · 2026-04-15 07:14:28

43

Views

A question related to abelian extensions

Published on 15 Apr 2026 - 7:14

score 330 · Answer 7 · 2026-04-14 08:43:50

330

Views

How can I prove that $\sqrt{2}$ is not inside Q($\sqrt{5 + \sqrt{5}}$)?

Published on 14 Apr 2026 - 8:43

score 114 · Answer 8 · 2026-04-10 22:28:42

114

Views

Criterion for finite Galois extension

Published on 10 Apr 2026 - 22:28

score 77 · Answer 9 · 2026-04-12 01:44:57

77

Views

What does it mean when one talks about splitting field of a multivariable polynomial? And then, Galois group of that splitting field?

Published on 12 Apr 2026 - 1:44

score 66 · Answer 10 · 2026-04-12 10:03:29

66

Views

Proving the irreducibility of a polynomial based on its Galois group

Published on 12 Apr 2026 - 10:03

score 218 · Answer 11 · 2026-04-16 10:23:18

218

Views

E/F is Galois ext with $[E:F]=p^2$ and its Galois group is not cyclic, then $\exists K$ a proper subfield of $E$.

Published on 16 Apr 2026 - 10:23

score 206 · Answer 12 · 2026-04-09 04:33:08

206

Views

Equivalent Definitions of Field Trace of Galois Extension

Published on 09 Apr 2026 - 4:33

score 166 · Answer 13 · 2026-04-14 07:33:24

166

Views

splitting field of separable and irreducible polynomial: does isomorphism of Galois subgroups imply isomorphism of subfields?

Published on 14 Apr 2026 - 7:33

score 171 · Answer 14 · 2026-04-15 08:31:08

171

Views

Splitting field of a degree 4 irreducible polynomial in $\mathbb{Q}[x]$ with two real roots and two non real roots

Published on 15 Apr 2026 - 8:31

score 63 · Answer 15 · 2026-04-14 03:22:43

63

Views

Degree of a polynomial zero over the simple extension attained by adjoining another zero.

Published on 14 Apr 2026 - 3:22

List Question

Elements of Galois group map roots of minimal polynomial to which other roots?

Can inseparable elements “appear” in the residue field of the Galois closure of a field extension with separable residue field extension?

Suppose $K$ is a Galois extension of $F$. Consider $E/F$ a finite extension such that $K\cap E=F$. Show that $[KE:K]=[E:F]$.

Existence of a Field not containing $\sqrt{2}$, such that any finite extension is cyclic.

Galois group for $\operatorname{Gal}(\mathbb{Q}(\zeta_n + \zeta_n^{-1})/\mathbb{Q})$

A question related to abelian extensions

How can I prove that $\sqrt{2}$ is not inside Q($\sqrt{5 + \sqrt{5}}$)?

Criterion for finite Galois extension

What does it mean when one talks about splitting field of a multivariable polynomial? And then, Galois group of that splitting field?

Proving the irreducibility of a polynomial based on its Galois group

E/F is Galois ext with $[E:F]=p^2$ and its Galois group is not cyclic, then $\exists K$ a proper subfield of $E$.

Equivalent Definitions of Field Trace of Galois Extension

splitting field of separable and irreducible polynomial: does isomorphism of Galois subgroups imply isomorphism of subfields?

Splitting field of a degree 4 irreducible polynomial in $\mathbb{Q}[x]$ with two real roots and two non real roots

Degree of a polynomial zero over the simple extension attained by adjoining another zero.

Trending Questions

Popular # Hahtags

Popular Questions