Question

Splitting field of $f(x)=x^7-3$ over $\mathbb{Q}$ and its degree

score 182 · Answer 1 · 2026-03-29 08:35:37

182

Views

Splitting field of $f(x)=x^7-3$ over $\mathbb{Q}$ and its degree

Published on 29 Mar 2026 - 8:35

score 287 · Answer 2 · 2019-10-14 07:36:27

287

Views

$\mathbb{Q}(\sqrt{p^*})$ is the only quadratic extension of $\mathbb{Q}$ contained in $\mathbb{Q}(\zeta_{p^n})$.

Published on 14 Oct 2019 - 7:36

score 29 · Answer 3 · 2019-10-14 21:37:52

29

Views

Isomorphism between algebraic extensions and irreducible polynomials

Published on 14 Oct 2019 - 21:37

score 42 · Answer 4 · 2026-04-01 00:26:53

42

Views

With field extension is odd the nonsquare element in $GF(p)$ is also a nonsquare in $GF(p^e)$ where $p$ is odd prime

Published on 01 Apr 2026 - 0:26

score 33 · Answer 5 · 2019-10-17 05:50:53

33

Views

a result about minimal polynomial and field extension

Published on 17 Oct 2019 - 5:50

score 44 · Answer 6 · 2019-10-18 06:00:43

44

Views

Find the degree of a field extension and proving polynomial irreducible

Published on 18 Oct 2019 - 6:00

score 409 · Answer 7 · 2019-10-18 19:31:32

409

Views

Basis of extension of scalars

Published on 18 Oct 2019 - 19:31

score 243 · Answer 8 · 2026-03-25 06:29:06

243

Views

Field elements which become $n$th powers after adjoining an $n$th root of unity

Published on 25 Mar 2026 - 6:29

score 75 · Answer 9 · 2026-02-23 04:58:21

75

Views

If $L/K$ is a finite separable extension and $P \in K[X], Q \in L[X]$, then $P = Q^n \Rightarrow Q \in K[X]$

Published on 23 Feb 2026 - 4:58

score 338 · Answer 10 · 2026-04-01 02:02:52

338

Views

Prove that $x^3+2y^3+4z^3\equiv6xyz \pmod{7} \Rightarrow x\equiv y\equiv z\equiv 0 \pmod{7}$

Published on 01 Apr 2026 - 2:02

score 136 · Answer 11 · 2026-03-29 08:35:39

136

Views

Confusion about a proof of every irreducible polynomial has a root in a field extension

Published on 29 Mar 2026 - 8:35

score 88 · Answer 12 · 2019-10-21 07:27:02

88

Views

Does there exist a field $K$ and $x \in K$ with $K(x^{1/4})=K(x^{1/2}) \neq K$

Published on 21 Oct 2019 - 7:27

score 63 · Answer 13 · 2026-03-28 02:42:52

63

Views

What is known about the quadratic closure of $\mathbb{Q}_p$?

Published on 28 Mar 2026 - 2:42

score 22 · Answer 14 · 2019-10-23 03:07:31

22

Views

Degree of the field extensions corresponding to the points trisecting a line

Published on 23 Oct 2019 - 3:07

score 114 · Answer 15 · 2019-10-25 12:57:09

114

Views

Are there any number fields that extend $\mathbb C$?

Published on 25 Oct 2019 - 12:57

List Question

Splitting field of $f(x)=x^7-3$ over $\mathbb{Q}$ and its degree

$\mathbb{Q}(\sqrt{p^*})$ is the only quadratic extension of $\mathbb{Q}$ contained in $\mathbb{Q}(\zeta_{p^n})$.

Isomorphism between algebraic extensions and irreducible polynomials

With field extension is odd the nonsquare element in $GF(p)$ is also a nonsquare in $GF(p^e)$ where $p$ is odd prime

a result about minimal polynomial and field extension

Find the degree of a field extension and proving polynomial irreducible

Basis of extension of scalars

Field elements which become $n$th powers after adjoining an $n$th root of unity

If $L/K$ is a finite separable extension and $P \in K[X], Q \in L[X]$, then $P = Q^n \Rightarrow Q \in K[X]$

Prove that $x^3+2y^3+4z^3\equiv6xyz \pmod{7} \Rightarrow x\equiv y\equiv z\equiv 0 \pmod{7}$

Confusion about a proof of every irreducible polynomial has a root in a field extension

Does there exist a field $K$ and $x \in K$ with $K(x^{1/4})=K(x^{1/2}) \neq K$

What is known about the quadratic closure of $\mathbb{Q}_p$?

Degree of the field extensions corresponding to the points trisecting a line

Are there any number fields that extend $\mathbb C$?

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