Question

$F$ is a field and $\alpha$ is any element. Then $[F(\alpha) :F(\alpha^3)]=1 \mbox{ or } 3$.

score 161 · Answer 1 · 2026-04-16 20:56:41

161

Views

$F$ is a field and $\alpha$ is any element. Then $[F(\alpha) :F(\alpha^3)]=1 \mbox{ or } 3$.

Published on 16 Apr 2026 - 20:56

score 63 · Answer 2 · 2026-04-16 08:58:04

63

Views

Why is : $ \operatorname{tr}\deg_K L = \dim \operatorname{Gal} ( \mathcal{L} ) $?

Published on 16 Apr 2026 - 8:58

score 658 · Answer 3 · 2026-04-12 20:21:16

658

Views

Galois group over $\mathbb C(t)$

Published on 12 Apr 2026 - 20:21

score 131 · Answer 4 · 2026-04-14 04:23:24

131

Views

If $3$ divides $p^n - 1$ does $\mathbf{F}_{p^n}$ contain a primitive third root of unity?

Published on 14 Apr 2026 - 4:23

score 806 · Answer 5 · 2026-04-13 17:18:48

806

Views

Total orderings on $\mathbb{Q}(\sqrt2)$

Published on 13 Apr 2026 - 17:18

score 82 · Answer 6 · 2026-04-14 12:38:39

82

Views

Show that $\mathscr{m}_{p}$ is the only maximal ideal of $\mathscr{O}_{p}$

Published on 14 Apr 2026 - 12:38

score 189 · Answer 7 · 2026-04-12 15:56:05

189

Views

A separable field extension of degree a product of two primes

Published on 12 Apr 2026 - 15:56

score 99 · Answer 8 · 2026-04-14 19:04:08

99

Views

Subrings between $\mathbb{Q}$ and $\mathbb{Q}[\sqrt{2}]$.

Published on 14 Apr 2026 - 19:04

score 1.3k · Answer 9 · 2026-04-15 23:51:58

1.3k

Views

Degree of $\Bbb R$ over $\Bbb Q(B)$, where $B$ is a $\Bbb Q(a)$-basis $(a \in \{\sqrt 2, e\})$

Published on 15 Apr 2026 - 23:51

score 297 · Answer 10 · 2026-04-15 03:23:44

297

Views

Is there a subfield $F$ of $\Bbb R$ such that there is an embedding $F(x) \hookrightarrow F$?

Published on 15 Apr 2026 - 3:23

score 1.4k · Answer 11 · 2026-03-25 19:10:56

1.4k

Views

Is $\Bbb Q(\sqrt 2, e)$ a simple extension of $\Bbb Q$?

Published on 25 Mar 2026 - 19:10

score 703 · Answer 12 · 2026-04-14 10:21:04

703

Views

degree of K(x) over K(F/G)

Published on 14 Apr 2026 - 10:21

score 475 · Answer 13 · 2026-04-11 22:07:37

475

Views

Definition primitive polynomial

Published on 11 Apr 2026 - 22:07

score 194 · Answer 14 · 2026-04-15 23:36:53

194

Views

Is it true that $F[(X_{\alpha})_{\alpha \in A}] \cong F[(X_{\beta})_{\beta \in B}] \implies |A|=|B|$, when $F$ is a subring of $\Bbb R$?

Published on 15 Apr 2026 - 23:36

score 172 · Answer 15 · 2026-04-14 06:46:30

172

Views

What is $ \mathcal{P} \mathrm{er} (X) / \mathbb{Q} $?

Published on 14 Apr 2026 - 6:46

List Question

$F$ is a field and $\alpha$ is any element. Then $[F(\alpha) :F(\alpha^3)]=1 \mbox{ or } 3$.

Why is : $ \operatorname{tr}\deg_K L = \dim \operatorname{Gal} ( \mathcal{L} ) $?

Galois group over $\mathbb C(t)$

If $3$ divides $p^n - 1$ does $\mathbf{F}_{p^n}$ contain a primitive third root of unity?

Total orderings on $\mathbb{Q}(\sqrt2)$

Show that $\mathscr{m}_{p}$ is the only maximal ideal of $\mathscr{O}_{p}$

A separable field extension of degree a product of two primes

Subrings between $\mathbb{Q}$ and $\mathbb{Q}[\sqrt{2}]$.

Degree of $\Bbb R$ over $\Bbb Q(B)$, where $B$ is a $\Bbb Q(a)$-basis $(a \in \{\sqrt 2, e\})$

Is there a subfield $F$ of $\Bbb R$ such that there is an embedding $F(x) \hookrightarrow F$?

Is $\Bbb Q(\sqrt 2, e)$ a simple extension of $\Bbb Q$?

degree of K(x) over K(F/G)

Definition primitive polynomial

Is it true that $F[(X_{\alpha})_{\alpha \in A}] \cong F[(X_{\beta})_{\beta \in B}] \implies |A|=|B|$, when $F$ is a subring of $\Bbb R$?

What is $ \mathcal{P} \mathrm{er} (X) / \mathbb{Q} $?

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