Question

Existence of a certain Galois extension

score 95 · Answer 1 · 2015-11-22 14:14:17

95

Views

Existence of a certain Galois extension

Published on 22 Nov 2015 - 14:14

score 62 · Answer 2 · 2015-11-25 18:01:10

62

Views

What is the degree of this extension?

Published on 25 Nov 2015 - 18:01

score 256 · Answer 3 · 2015-11-27 06:10:59

256

Views

Is there a connection between primitive elements (for field extensions) and cyclic vectors (in linear algebra)

Published on 27 Nov 2015 - 6:10

score 227 · Answer 4 · 2015-11-27 22:38:37

227

Views

Galois' theory: fixed subfield formula.

Published on 27 Nov 2015 - 22:38

score 141 · Answer 5 · 2026-04-10 23:34:22

141

Views

Complexification of $\mathbb{Z}$ using tensor products

Published on 10 Apr 2026 - 23:34

score 45 · Answer 6 · 2015-11-29 02:44:12

45

Views

Prove that if there exists an ascending chain of subfields of E such that [E_(i):E_(i-1)]=2 for all i if and only if [E:K] is a power of 2.

Published on 29 Nov 2015 - 2:44

score 471 · Answer 7 · 2015-11-29 04:15:35

471

Views

Using Galois theory, determine the number of subfields of an extension field

Published on 29 Nov 2015 - 4:15

score 684 · Answer 8 · 2015-11-29 06:12:09

684

Views

Is there an alternative proof of the abel-ruffini theorem?

Published on 29 Nov 2015 - 6:12

score 1.6k · Answer 9 · 2015-11-29 06:14:03

Let $\alpha, \beta \in \mathbb{C}$, such that $\alpha + \beta$, and $\alpha\beta$ are algebraic. Show that $\alpha$ and $\beta$ are algebraic.

score 137 · Answer 10 · 2015-11-30 02:22:10

137

Views

Suppose $F = \mathbb{Q}(\alpha_1,...,\alpha_n)$, where $\alpha_i^2 \in \mathbb{Q}$, for $i = 1,...,n$. Prove that $\sqrt[3]2 \not\in F$.

Published on 30 Nov 2015 - 2:22

score 541 · Answer 11 · 2015-11-30 04:20:48

541

Views

$F$-linear maps $K \to K$ as a vector space over $K$(!), where $K/F$ is a finite-dimensional field extension

Published on 30 Nov 2015 - 4:20

score 64 · Answer 12 · 2026-03-28 03:25:19

64

Views

Let $f(\lambda) =\lambda^4 - 4\lambda^2 + 2 \in \mathbb{Q}[\lambda]$, let $E$ be the splitting field, find $E$ and $[E : \mathbb{Q}]$

Published on 28 Mar 2026 - 3:25

score 1.2k · Answer 13 · 2026-03-28 03:26:01

1.2k

Views

Finite field isomorphic to $\mathbb F_{p^n}$.

Published on 28 Mar 2026 - 3:26

score 1k · Answer 14 · 2015-12-03 16:42:49

1k

Views

Why is $\mathbb{Q}(\sqrt[4]{2}) $ is not normal over $\mathbb{Q}$?

Published on 03 Dec 2015 - 16:42

score 1k · Answer 15 · 2015-12-03 18:12:06

1k

Views

Find a counterexample to the statement "If $K\subset M\subset L$ are fields and $L$ is normal over $K$, then $M$ normal over $K$"

Published on 03 Dec 2015 - 18:12

List Question

Existence of a certain Galois extension

What is the degree of this extension?

Is there a connection between primitive elements (for field extensions) and cyclic vectors (in linear algebra)

Galois' theory: fixed subfield formula.

Complexification of $\mathbb{Z}$ using tensor products

Prove that if there exists an ascending chain of subfields of E such that [E_(i):E_(i-1)]=2 for all i if and only if [E:K] is a power of 2.

Using Galois theory, determine the number of subfields of an extension field

Is there an alternative proof of the abel-ruffini theorem?

Let $\alpha, \beta \in \mathbb{C}$, such that $\alpha + \beta$, and $\alpha\beta$ are algebraic. Show that $\alpha$ and $\beta$ are algebraic.

Suppose $F = \mathbb{Q}(\alpha_1,...,\alpha_n)$, where $\alpha_i^2 \in \mathbb{Q}$, for $i = 1,...,n$. Prove that $\sqrt[3]2 \not\in F$.

$F$-linear maps $K \to K$ as a vector space over $K$(!), where $K/F$ is a finite-dimensional field extension

Let $f(\lambda) =\lambda^4 - 4\lambda^2 + 2 \in \mathbb{Q}[\lambda]$, let $E$ be the splitting field, find $E$ and $[E : \mathbb{Q}]$

Finite field isomorphic to $\mathbb F_{p^n}$.

Why is $\mathbb{Q}(\sqrt[4]{2}) $ is not normal over $\mathbb{Q}$?

Find a counterexample to the statement "If $K\subset M\subset L$ are fields and $L$ is normal over $K$, then $M$ normal over $K$"

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