Question

Show that for every $n$-primary root of unity that ${\rm Gal}(K(\zeta),\Bbb Q)$ is solvable.

score 55 · Answer 1 · 2026-04-14 13:05:44

55

Views

Show that for every $n$-primary root of unity that ${\rm Gal}(K(\zeta),\Bbb Q)$ is solvable.

Published on 14 Apr 2026 - 13:05

score 34 · Answer 2 · 2026-04-16 13:25:44

34

Views

What is the meaning of roots for $p(x)$ derived from the extension field $F[x]/p(x)$?

Published on 16 Apr 2026 - 13:25

score 79 · Answer 3 · 2026-04-17 01:05:28

79

Views

Let $K/F$ and $a,b \in K$ algebraic over $F$ and $[F(a):F]=m ,[F(b):F]=n$ then show that degree of $a + b, ab, a − b , ab^{−1}$ atmost $mn$ over $F$

Published on 17 Apr 2026 - 1:05

score 75 · Answer 4 · 2026-04-14 07:50:34

75

Views

Intermediate Fields of Rational Functions

Published on 14 Apr 2026 - 7:50

score 318 · Answer 5 · 2026-04-15 17:54:52

318

Views

$F(\alpha)$ is isomorphic to the field $F(x)$ of rational functions over $F$ in the indeterminate $x$ where $\alpha$ is transcendental over $F$

Published on 15 Apr 2026 - 17:54

score 157 · Answer 6 · 2026-04-16 04:23:30

157

Views

If $\alpha ,\beta$ algebraic over $F$ then there exist a isomorphism $\psi:F(\alpha) \to F(\beta) $iff $\alpha,\beta$ have same minimal polynomial

Published on 16 Apr 2026 - 4:23

score 70 · Answer 7 · 2026-04-17 14:11:38

70

Views

In Quadratic Number Fields, $N(\mathfrak{q})=p^2\Leftrightarrow \mathfrak{q}=(p)$ inert?

Published on 17 Apr 2026 - 14:11

score 61 · Answer 8 · 2026-04-11 01:23:47

61

Views

Field extension over rationals

Published on 11 Apr 2026 - 1:23

score 324 · Answer 9 · 2026-04-15 16:47:24

324

Views

Given prime integer p, and positive integer n,show that there exists a finite field consisting of $p^n = q$ roots of $x^q − x$ over $\mathbb{Z}_p$

Published on 15 Apr 2026 - 16:47

score 115 · Answer 10 · 2026-04-14 19:21:23

115

Views

If there exists a primitive element of a finite extension a field, there are finite number of nested fields. Where is "primitiveness" used?

Published on 14 Apr 2026 - 19:21

score 87 · Answer 11 · 2026-04-17 07:18:09

87

Views

If $F= {\mathbb{Q}[x]}/{(x^5+5x^2-10)}$ then show that $[F:\mathbb{Q}]=5$.

Published on 17 Apr 2026 - 7:18

score 73 · Answer 12 · 2026-04-16 23:28:41

73

Views

Seperability degree and roots of $f=X^{p^2}-TX^p-T\in\mathbb{F}_p(T)[X]$

Published on 16 Apr 2026 - 23:28

score 119 · Answer 13 · 2026-04-11 16:09:14

119

Views

Explanation behind $\text{Gal}(K/K^H)=H$.

Published on 11 Apr 2026 - 16:09

score 136 · Answer 14 · 2026-04-10 21:35:24

136

Views

Radicals in a Cyclotomic Field Extension

Published on 10 Apr 2026 - 21:35

score 238 · Answer 15 · 2026-04-16 20:36:21

238

Views

$\alpha$ is transcendental and there exists some $\beta$ such that $f(\beta) =\alpha$. Show that $\beta$ is transcendental.

Published on 16 Apr 2026 - 20:36

List Question

Show that for every $n$-primary root of unity that ${\rm Gal}(K(\zeta),\Bbb Q)$ is solvable.

What is the meaning of roots for $p(x)$ derived from the extension field $F[x]/p(x)$?

Let $K/F$ and $a,b \in K$ algebraic over $F$ and $[F(a):F]=m ,[F(b):F]=n$ then show that degree of $a + b, ab, a − b , ab^{−1}$ atmost $mn$ over $F$

Intermediate Fields of Rational Functions

$F(\alpha)$ is isomorphic to the field $F(x)$ of rational functions over $F$ in the indeterminate $x$ where $\alpha$ is transcendental over $F$

If $\alpha ,\beta$ algebraic over $F$ then there exist a isomorphism $\psi:F(\alpha) \to F(\beta) $iff $\alpha,\beta$ have same minimal polynomial

In Quadratic Number Fields, $N(\mathfrak{q})=p^2\Leftrightarrow \mathfrak{q}=(p)$ inert?

Field extension over rationals

Given prime integer p, and positive integer n,show that there exists a finite field consisting of $p^n = q$ roots of $x^q − x$ over $\mathbb{Z}_p$

If there exists a primitive element of a finite extension a field, there are finite number of nested fields. Where is "primitiveness" used?

If $F= {\mathbb{Q}[x]}/{(x^5+5x^2-10)}$ then show that $[F:\mathbb{Q}]=5$.

Seperability degree and roots of $f=X^{p^2}-TX^p-T\in\mathbb{F}_p(T)[X]$

Explanation behind $\text{Gal}(K/K^H)=H$.

Radicals in a Cyclotomic Field Extension

$\alpha$ is transcendental and there exists some $\beta$ such that $f(\beta) =\alpha$. Show that $\beta$ is transcendental.

Trending Questions

Popular # Hahtags

Popular Questions