Question

Determining all extensions of a field morphism

score 136 · Answer 1 · 2023-06-27 22:43:20

136

Views

Determining all extensions of a field morphism

Published on 27 Jun 2023 - 22:43

score 43 · Answer 2 · 2023-06-28 14:53:41

43

Views

Free, linearly disjoint field extensions and algebraic/separable closures

Published on 28 Jun 2023 - 14:53

score 80 · Answer 3 · 2023-06-28 18:12:24

80

Views

Degree of $\xi+\xi^5+\xi^8$ where $\xi$ is primitive 13th root

Published on 28 Jun 2023 - 18:12

score 106 · Answer 4 · 2023-06-29 02:51:48

106

Views

How to determine the degree of the extension $\mathbb{Q}(\sqrt[3] 2,i)$ over $\mathbb{Q}$? and what is the form of these?

Published on 29 Jun 2023 - 2:51

score 93 · Answer 5 · 2023-06-29 11:50:19

93

Views

$\mathbb{Q}(\alpha, \sqrt 2)$ = $\mathbb{Q}(\alpha \sqrt 2)$, where $\alpha$ is a root of $ x^3 −x^2 + 1$?

Published on 29 Jun 2023 - 11:50

score 100 · Answer 6 · 2026-03-26 04:35:05

100

Views

Is the splitting field of $x^3+2x^2-x-3$ a totally ramified extension of $\mathbb Q_5$?

Published on 26 Mar 2026 - 4:35

score 152 · Answer 7 · 2026-03-28 08:09:25

152

Views

Prove irreducible cubic polynomial over $\mathbb{Q}$ with a cyclic galois group has real roots

Published on 28 Mar 2026 - 8:09

score 29 · Answer 8 · 2023-07-03 06:37:59

29

Views

How to factorize $x^p-a$ in $K[x]$ over $K(\xi,\sqrt[p]a)$ where $a\in K$ and char$K=p$, $\xi$ is a primitive $p$-th root of unity and $p$ is a prime?

Published on 03 Jul 2023 - 6:37

score 23 · Answer 9 · 2026-02-23 08:32:57

23

Views

prove $\deg_{\alpha,L}\mid\deg_{\alpha,K}$ if $\alpha$ is separable and $K(\alpha)/K$ is normal

Published on 23 Feb 2026 - 8:32

score 64 · Answer 10 · 2026-02-23 08:31:45

64

Views

Proof that on infinite fields, finite separable extensions are all simple.

Published on 23 Feb 2026 - 8:31

score 71 · Answer 11 · 2026-04-06 00:20:27

71

Views

$F$ is a finite field whose order is a power of 3, then $\sqrt{-1} \in F$ if and only if $\sqrt[4]{-1} \in F$

Published on 06 Apr 2026 - 0:20

score 60 · Answer 12 · 2026-02-23 02:48:22

60

Views

Show $\mathbb{Q}(\sqrt{3+\sqrt{3}})/\mathbb{Q}$ is not a normal extension and find it's normal closure

Published on 23 Feb 2026 - 2:48

score 37 · Answer 13 · 2023-07-07 15:52:58

37

Views

number of extensions of a field embedding after taking a finite extension of the domain

Published on 07 Jul 2023 - 15:52

score 44 · Answer 14 · 2023-07-07 17:58:25

44

Views

Quick question on way to find the degree of certain field extensions

Published on 07 Jul 2023 - 17:58

score 31 · Answer 15 · 2026-04-01 10:24:43

31

Views

characterization of finite extension of $\mathbb{Q}$ by maximal ideals

Published on 01 Apr 2026 - 10:24

List Question

Determining all extensions of a field morphism

Free, linearly disjoint field extensions and algebraic/separable closures

Degree of $\xi+\xi^5+\xi^8$ where $\xi$ is primitive 13th root

How to determine the degree of the extension $\mathbb{Q}(\sqrt[3] 2,i)$ over $\mathbb{Q}$? and what is the form of these?

$\mathbb{Q}(\alpha, \sqrt 2)$ = $\mathbb{Q}(\alpha \sqrt 2)$, where $\alpha$ is a root of $ x^3 −x^2 + 1$?

Is the splitting field of $x^3+2x^2-x-3$ a totally ramified extension of $\mathbb Q_5$?

Prove irreducible cubic polynomial over $\mathbb{Q}$ with a cyclic galois group has real roots

How to factorize $x^p-a$ in $K[x]$ over $K(\xi,\sqrt[p]a)$ where $a\in K$ and char$K=p$, $\xi$ is a primitive $p$-th root of unity and $p$ is a prime?

prove $\deg_{\alpha,L}\mid\deg_{\alpha,K}$ if $\alpha$ is separable and $K(\alpha)/K$ is normal

Proof that on infinite fields, finite separable extensions are all simple.

$F$ is a finite field whose order is a power of 3, then $\sqrt{-1} \in F$ if and only if $\sqrt[4]{-1} \in F$

Show $\mathbb{Q}(\sqrt{3+\sqrt{3}})/\mathbb{Q}$ is not a normal extension and find it's normal closure

number of extensions of a field embedding after taking a finite extension of the domain

Quick question on way to find the degree of certain field extensions

characterization of finite extension of $\mathbb{Q}$ by maximal ideals

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