Question

about square elements in finite field

score 145 · Answer 1 · 2026-03-27 01:43:08

about square elements in finite field

Published on 27 Mar 2026 - 1:43

score 26 · Answer 2 · 2018-08-30 11:38:04

If $\varepsilon$ is a $n$-th root of unity, then it is a $d$-th primitive root of unity for some $d | n$, in a special case.

score 665 · Answer 3 · 2026-03-27 03:42:20

665

Views

Every algebraic extension of a finite field is normal?

Published on 27 Mar 2026 - 3:42

score 329 · Answer 4 · 2026-03-29 12:12:06

329

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Show that $ \mathbb{Q}[x]/(x^4 - 6x^2 + 4) \simeq \mathbb{Q}(\sqrt{2}, \sqrt{5})$

Published on 29 Mar 2026 - 12:12

score 85 · Answer 5 · 2018-08-31 05:35:18

85

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If F is a subfield of $\mathbb{R}$ and $\sqrt{2} +\sqrt{3} \in F$ then both $\sqrt{2}$ and $\sqrt{3}$ in F?

Published on 31 Aug 2018 - 5:35

score 261 · Answer 6 · 2026-03-29 12:05:18

261

Views

Proving these two statements are equivalent in this field of characteristic $\neq 2$

Published on 29 Mar 2026 - 12:05

score 96 · Answer 7 · 2026-03-25 14:00:29

96

Views

Example of when $E^{H} \neq E^{\text{Aut}(E/E^H)}$?

Published on 25 Mar 2026 - 14:00

score 104 · Answer 8 · 2026-03-27 01:42:35

104

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About quadratic forms

Published on 27 Mar 2026 - 1:42

score 1k · Answer 9 · 2026-03-29 08:13:45

1k

Views

Do extension fields always belong to a bigger field?

Published on 29 Mar 2026 - 8:13

score 94 · Answer 10 · 2026-03-23 02:39:39

94

Views

How to construct $\mathbb{F}_p(\zeta)$ with MAGMA?

Published on 23 Mar 2026 - 2:39

score 468 · Answer 11 · 2026-03-25 16:40:15

468

Views

Explicit absolute value of $\mathbb{C}_p$ and completion of algebraic closure of $\mathbb{F}_p((t))$

Published on 25 Mar 2026 - 16:40

score 1.5k · Answer 12 · 2026-03-25 17:44:34

1.5k

Views

If $F$ is a subfield of an algebraically closed field $K$, then the algebraic closure $\overline{F}$ of $F$ in $K$ is also algebraically closed.

Published on 25 Mar 2026 - 17:44

score 189 · Answer 13 · 2026-03-29 13:41:09

189

Views

Finite-Galois-theoretic characterization of formally real fields?

Published on 29 Mar 2026 - 13:41

score 688 · Answer 14 · 2018-09-06 04:38:05

688

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Show that (x+y)^3 is not equal to x^3+y^3 for some x and y in a field F

Published on 06 Sep 2018 - 4:38

score 28 · Answer 15 · 2018-09-06 10:35:41

28

Views

Extension field obtained from polynomial

Published on 06 Sep 2018 - 10:35

List Question

about square elements in finite field

If $\varepsilon$ is a $n$-th root of unity, then it is a $d$-th primitive root of unity for some $d | n$, in a special case.

Every algebraic extension of a finite field is normal?

Show that $ \mathbb{Q}[x]/(x^4 - 6x^2 + 4) \simeq \mathbb{Q}(\sqrt{2}, \sqrt{5})$

If F is a subfield of $\mathbb{R}$ and $\sqrt{2} +\sqrt{3} \in F$ then both $\sqrt{2}$ and $\sqrt{3}$ in F?

Proving these two statements are equivalent in this field of characteristic $\neq 2$

Example of when $E^{H} \neq E^{\text{Aut}(E/E^H)}$?

About quadratic forms

Do extension fields always belong to a bigger field?

How to construct $\mathbb{F}_p(\zeta)$ with MAGMA?

Explicit absolute value of $\mathbb{C}_p$ and completion of algebraic closure of $\mathbb{F}_p((t))$

If $F$ is a subfield of an algebraically closed field $K$, then the algebraic closure $\overline{F}$ of $F$ in $K$ is also algebraically closed.

Finite-Galois-theoretic characterization of formally real fields?

Show that (x+y)^3 is not equal to x^3+y^3 for some x and y in a field F

Extension field obtained from polynomial

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