Question

Is $K =\mathbb{Q}(i\sqrt{2}) \subset L=K(\sqrt[3]{6+i})$ normal field extension?

score 43 · Answer 1 · 2026-04-15 08:35:48

43

Views

Is $K =\mathbb{Q}(i\sqrt{2}) \subset L=K(\sqrt[3]{6+i})$ normal field extension?

Published on 15 Apr 2026 - 8:35

score 26 · Answer 2 · 2026-04-12 18:45:10

26

Views

Are the following extensions normal?

Published on 12 Apr 2026 - 18:45

score 88 · Answer 3 · 2026-04-16 04:28:32

88

Views

If $K/F$ is Galois, and the coefficients of the monic $f \in K[x]$ generates $K$, then $\prod_{\sigma \in Gal(K/F)}\sigma f \in F[x]$

Published on 16 Apr 2026 - 4:28

score 36 · Answer 4 · 2026-04-11 11:30:35

36

Views

How do splitting fields over different field extensions "fit" inside each other

Published on 11 Apr 2026 - 11:30

score 77 · Answer 5 · 2026-04-15 13:10:37

77

Views

A basis of a field extension contained in a subring

Published on 15 Apr 2026 - 13:10

score 71 · Answer 6 · 2026-04-14 18:15:03

71

Views

Galois: Why does $\{1,f,f^2\}$ correspond to $\mathbb{Q}(\omega)$?

Published on 14 Apr 2026 - 18:15

score 56 · Answer 7 · 2026-04-13 14:50:45

56

Views

Can we always find field extensions of a given number field and a given degree?

Published on 13 Apr 2026 - 14:50

score 81 · Answer 8 · 2026-04-14 05:36:47

81

Views

$L$ is an extension of $K$, if $L$ is a $K$-algebra

Published on 14 Apr 2026 - 5:36

score 115 · Answer 9 · 2026-04-16 08:01:39

115

Views

Show $Gal(E/\mathbb{Q})\cong \mathbb{\mathbb{Z_2\times Z_2}}$

Published on 16 Apr 2026 - 8:01

score 280 · Answer 10 · 2026-04-16 00:14:53

280

Views

How to prove that the polynomial $x^2 + x + 1$ is irreducible over $\mathbb Q(\sqrt[3]{2})$?

Published on 16 Apr 2026 - 0:14

score 290 · Answer 11 · 2026-04-16 06:32:58

290

Views

Determine the splitting field and its degree over $\mathbb Q$ for $x^6 - 4.$

Published on 16 Apr 2026 - 6:32

score 101 · Answer 12 · 2026-04-14 18:32:31

101

Views

Does there exist two different fields over $F$ such that they have the same intermediate fields?

Published on 14 Apr 2026 - 18:32

score 27 · Answer 13 · 2026-04-13 01:26:18

27

Views

Comprehension question regarding transcendent elements and the rational function field

Published on 13 Apr 2026 - 1:26

score 85 · Answer 14 · 2026-04-13 17:11:35

85

Views

An infinite family of Artin-Schreier polynomials which all split in $\mathbf{F}_q(\!(\theta)\!)$

Published on 13 Apr 2026 - 17:11

score 47 · Answer 15 · 2026-04-13 09:36:32

47

Views

Are this elements algebraic?

Published on 13 Apr 2026 - 9:36

List Question

Is $K =\mathbb{Q}(i\sqrt{2}) \subset L=K(\sqrt[3]{6+i})$ normal field extension?

Are the following extensions normal?

If $K/F$ is Galois, and the coefficients of the monic $f \in K[x]$ generates $K$, then $\prod_{\sigma \in Gal(K/F)}\sigma f \in F[x]$

How do splitting fields over different field extensions "fit" inside each other

A basis of a field extension contained in a subring

Galois: Why does $\{1,f,f^2\}$ correspond to $\mathbb{Q}(\omega)$?

Can we always find field extensions of a given number field and a given degree?

$L$ is an extension of $K$, if $L$ is a $K$-algebra

Show $Gal(E/\mathbb{Q})\cong \mathbb{\mathbb{Z_2\times Z_2}}$

How to prove that the polynomial $x^2 + x + 1$ is irreducible over $\mathbb Q(\sqrt[3]{2})$?

Determine the splitting field and its degree over $\mathbb Q$ for $x^6 - 4.$

Does there exist two different fields over $F$ such that they have the same intermediate fields?

Comprehension question regarding transcendent elements and the rational function field

An infinite family of Artin-Schreier polynomials which all split in $\mathbf{F}_q(\!(\theta)\!)$

Are this elements algebraic?

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