Question

Why are the Galois groups that correspond to extensions which adjoin primitive roots of unity given by the group of units mod n

score 314 · Answer 1 · 2026-03-25 13:34:20

314

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Why are the Galois groups that correspond to extensions which adjoin primitive roots of unity given by the group of units mod n

Published on 25 Mar 2026 - 13:34

score 499 · Answer 2 · 2026-03-25 22:26:08

499

Views

When degree of splitting field equals n factorial

Published on 25 Mar 2026 - 22:26

score 609 · Answer 3 · 2026-04-05 23:28:30

609

Views

Let $T$ be a linear operator on a finite-dimensional vector space, $f$ is any polynomial, find out the relation between eigenvalues of $f(T)$ and $T$.

Published on 05 Apr 2026 - 23:28

score 939 · Answer 4 · 2026-03-26 17:32:55

939

Views

Tensor product of Galois extension

Published on 26 Mar 2026 - 17:32

score 75 · Answer 5 · 2026-03-27 00:02:21

75

Views

Irreducibility of polynomials over some quadratic fields

Published on 27 Mar 2026 - 0:02

score 83 · Answer 6 · 2026-03-31 15:24:18

83

Views

Prove that $[E(u): F(u)] \leq [E:F]$.

Published on 31 Mar 2026 - 15:24

score 92 · Answer 7 · 2026-03-27 00:02:48

92

Views

Show some polynomial satisfies Eisenstein's Criterion

Published on 27 Mar 2026 - 0:02

score 227 · Answer 8 · 2026-04-01 05:06:25

227

Views

some questions on finding the Galois group of the splitting field of $x^4-3$

Published on 01 Apr 2026 - 5:06

score 155 · Answer 9 · 2026-04-01 05:05:12

155

Views

$\mathbb{Q}[\sqrt[3]{2}]/\mathbb{Q}$ is separable but not normal, $\mathbb{F}_p(T)/\mathbb{F}_p(T^p)$ is normal but not separable

Published on 01 Apr 2026 - 5:05

score 325 · Answer 10 · 2026-03-26 18:06:22

325

Views

Points in the Fano plane

Published on 26 Mar 2026 - 18:06

score 175 · Answer 11 · 2026-02-23 03:01:17

175

Views

If $x$ and $y$ are complex numbers and $x+y$ , $xy$ are algebraic numbers then how to prove that $x$ and $y$ are also algebraic numbers?

Published on 23 Feb 2026 - 3:01

score 324 · Answer 12 · 2026-03-31 15:18:36

324

Views

Find degree of extension $Q$($\sqrt{1+\sqrt{-3}}$ + $\sqrt{1-\sqrt{-3}}$) over $Q$

Published on 31 Mar 2026 - 15:18

score 82 · Answer 13 · 2026-03-31 17:05:21

82

Views

A question on the Galois correspondance of $\sigma^2$ in $D_8$.

Published on 31 Mar 2026 - 17:05

score 563 · Answer 14 · 2026-03-28 08:35:37

563

Views

Automorphisms of the field of rational functions $\Bbb C(t)$

Published on 28 Mar 2026 - 8:35

score 173 · Answer 15 · 2026-03-25 02:59:09

173

Views

Efficient calculation of difference sets from finite fields

Published on 25 Mar 2026 - 2:59

List Question

Why are the Galois groups that correspond to extensions which adjoin primitive roots of unity given by the group of units mod n

When degree of splitting field equals n factorial

Let $T$ be a linear operator on a finite-dimensional vector space, $f$ is any polynomial, find out the relation between eigenvalues of $f(T)$ and $T$.

Tensor product of Galois extension

Irreducibility of polynomials over some quadratic fields

Prove that $[E(u): F(u)] \leq [E:F]$.

Show some polynomial satisfies Eisenstein's Criterion

some questions on finding the Galois group of the splitting field of $x^4-3$

$\mathbb{Q}[\sqrt[3]{2}]/\mathbb{Q}$ is separable but not normal, $\mathbb{F}_p(T)/\mathbb{F}_p(T^p)$ is normal but not separable

Points in the Fano plane

If $x$ and $y$ are complex numbers and $x+y$ , $xy$ are algebraic numbers then how to prove that $x$ and $y$ are also algebraic numbers?

Find degree of extension $Q$($\sqrt{1+\sqrt{-3}}$ + $\sqrt{1-\sqrt{-3}}$) over $Q$

A question on the Galois correspondance of $\sigma^2$ in $D_8$.

Automorphisms of the field of rational functions $\Bbb C(t)$

Efficient calculation of difference sets from finite fields

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