Question

Is this a correct argument for an irred. polynomial of deg $m$ stays irred. over a field extension of deg $n$ if $n$ and $m$ are co-prime?

score 93 · Answer 1 · 2026-03-31 07:12:10

93

Views

Is this a correct argument for an irred. polynomial of deg $m$ stays irred. over a field extension of deg $n$ if $n$ and $m$ are co-prime?

Published on 31 Mar 2026 - 7:12

score 32 · Answer 2 · 2016-10-02 17:17:30

32

Views

$K\subset L$ Galois-extension with $Gal(L/K)=G, ord(G)=p^2$ then there are $p+3$ subextensions

Published on 02 Oct 2016 - 17:17

score 1.4k · Answer 3 · 2016-10-03 15:32:04

1.4k

Views

How is the prime field "generated"?

Published on 03 Oct 2016 - 15:32

score 498 · Answer 4 · 2026-03-27 23:53:22

498

Views

Does there exist $\alpha \in \mathbb{R}$ and a field $F \subset \mathbb{R} $ such that $F(\alpha)=\mathbb{R}$?

Published on 27 Mar 2026 - 23:53

score 89 · Answer 5 · 2016-10-06 10:52:13

89

Views

Explicit expression minimal polynomial which is equal to characteristic.

Published on 06 Oct 2016 - 10:52

score 119 · Answer 6 · 2016-10-08 21:39:52

119

Views

How should $\mathbb{C}\triangleq\mathbb{R}[X]/(X^2+1)$ be read?

Published on 08 Oct 2016 - 21:39

score 242 · Answer 7 · 2026-03-31 07:06:22

242

Views

Polynomial irreducible over an extension with coprime degree.

Published on 31 Mar 2026 - 7:06

score 22 · Answer 8 · 2016-10-10 14:17:15

22

Views

Proving that $\Bbb{Q}(\xi^2 2^{2/5}+\xi^3 2^{3/5})=\Bbb{Q}(\xi2^{1/5})$

Published on 10 Oct 2016 - 14:17

score 57 · Answer 9 · 2016-10-10 21:06:06

57

Views

Can basic field theory be transposed over to group theory? (polynomials in a group-only setting)

Published on 10 Oct 2016 - 21:06

score 392 · Answer 10 · 2016-10-13 00:21:31

392

Views

Is $\mathbb{Q}(t):\mathbb{Q}$ a normal field extension?

Published on 13 Oct 2016 - 0:21

score 1.4k · Answer 11 · 2016-10-13 23:28:17

1.4k

Views

Degree of Field Extension $\mathbb{Q}(\sqrt[4]{2}):\mathbb{Q}(\sqrt{2})$

Published on 13 Oct 2016 - 23:28

score 180 · Answer 12 · 2026-03-27 00:37:45

180

Views

Find a splitting field extension for $t^3-5$ over $\mathbb{Z}_7$, $\mathbb{Z}_{11}$, and $\mathbb{Z}_{13}$

Published on 27 Mar 2026 - 0:37

score 132 · Answer 13 · 2016-10-14 01:31:05

132

Views

Suppose $M : L$ and $L : K$ are extensions, and that $\alpha \in M$ is algebraic over $K$. Does $[L(\alpha):L]$ always divide $[K(\alpha):K]$?

Published on 14 Oct 2016 - 1:31

score 112 · Answer 14 · 2016-10-14 11:39:44

112

Views

Show that $\lvert \mathbb{Q}(\sqrt2 , \sqrt{1+i}) : \mathbb{Q} \rvert = 8$

Published on 14 Oct 2016 - 11:39

score 132 · Answer 15 · 2016-10-14 14:01:54

132

Views

$\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$

Published on 14 Oct 2016 - 14:01

List Question

Is this a correct argument for an irred. polynomial of deg $m$ stays irred. over a field extension of deg $n$ if $n$ and $m$ are co-prime?

$K\subset L$ Galois-extension with $Gal(L/K)=G, ord(G)=p^2$ then there are $p+3$ subextensions

How is the prime field "generated"?

Does there exist $\alpha \in \mathbb{R}$ and a field $F \subset \mathbb{R} $ such that $F(\alpha)=\mathbb{R}$?

Explicit expression minimal polynomial which is equal to characteristic.

How should $\mathbb{C}\triangleq\mathbb{R}[X]/(X^2+1)$ be read?

Polynomial irreducible over an extension with coprime degree.

Proving that $\Bbb{Q}(\xi^2 2^{2/5}+\xi^3 2^{3/5})=\Bbb{Q}(\xi2^{1/5})$

Can basic field theory be transposed over to group theory? (polynomials in a group-only setting)

Is $\mathbb{Q}(t):\mathbb{Q}$ a normal field extension?

Degree of Field Extension $\mathbb{Q}(\sqrt[4]{2}):\mathbb{Q}(\sqrt{2})$

Find a splitting field extension for $t^3-5$ over $\mathbb{Z}_7$, $\mathbb{Z}_{11}$, and $\mathbb{Z}_{13}$

Suppose $M : L$ and $L : K$ are extensions, and that $\alpha \in M$ is algebraic over $K$. Does $[L(\alpha):L]$ always divide $[K(\alpha):K]$?

Show that $\lvert \mathbb{Q}(\sqrt2 , \sqrt{1+i}) : \mathbb{Q} \rvert = 8$

$\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$

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