Question

If $R/k$ is a ring extension, with $k$ a field, $R$ a integer domain, $[R:k]=n\in\mathbb{N}\implies R$ is a field

score 56 · Answer 1 · 2019-10-08 01:52:37

56

Views

If $R/k$ is a ring extension, with $k$ a field, $R$ a integer domain, $[R:k]=n\in\mathbb{N}\implies R$ is a field

Published on 08 Oct 2019 - 1:52

score 42 · Answer 2 · 2019-10-08 12:17:51

42

Views

$L/k$ and $K/k$ field extensions of $k$ with $[L:k]=m,[K:k]=n, (m,n)=1\implies L\cap K=k$

Published on 08 Oct 2019 - 12:17

score 147 · Answer 3 · 2026-03-25 15:22:45

147

Views

Galois Group of Ordered Field containing Square Roots

Published on 25 Mar 2026 - 15:22

score 132 · Answer 4 · 2019-10-08 18:07:48

132

Views

Prime degree extension and polynomial root

Published on 08 Oct 2019 - 18:07

score 332 · Answer 5 · 2026-03-29 06:55:23

332

Views

$x^5-2x^3+2x-2$ irreducible over $\mathbb{Q}(\sqrt[3]{2})$

Published on 29 Mar 2026 - 6:55

score 54 · Answer 6 · 2019-10-09 18:23:45

54

Views

$K/k$ field extension, $[K:k]=p$ prime, $f(X)\in [X]$ has degree $p+1$, $f$ has root in $K\iff f$ has root in $k$

Published on 09 Oct 2019 - 18:23

score 180 · Answer 7 · 2026-03-27 12:56:08

180

Views

How many roots of unity exists in $K=\Bbb Q_2(\sqrt{-3})$

Published on 27 Mar 2026 - 12:56

score 58 · Answer 8 · 2026-03-29 07:00:25

58

Views

$K/k$ field extension, $[K:k]=n,f(x)\in k[x]$ irreducible over $k$ with degree $m$, and $f$ has a root in $K\implies m$ divides $n$

Published on 29 Mar 2026 - 7:00

score 592 · Answer 9 · 2019-10-10 13:52:22

592

Views

About the Galois group of the polynomial $f(x)=x^4+ax^2+b$ over $\mathbb Q$

Published on 10 Oct 2019 - 13:52

score 45 · Answer 10 · 2026-03-29 06:55:42

45

Views

Finding the degree $[\mathbb{Q}(\sqrt[4]{3},\sqrt[5]{3}):\mathbb{Q}]$

Published on 29 Mar 2026 - 6:55

score 254 · Answer 11 · 2019-10-11 08:17:09

254

Views

Let $F \subseteq E$ be a field extension. Does $F$ isomorphic to $E$ imply $E=F$?

Published on 11 Oct 2019 - 8:17

score 174 · Answer 12 · 2026-03-26 08:14:38

174

Views

Finding splitting fields over $\mathbb{Q}(\sqrt{-3})$

Published on 26 Mar 2026 - 8:14

score 89 · Answer 13 · 2019-10-12 17:46:13

89

Views

Must a field extension contain an element of particular degree?

Published on 12 Oct 2019 - 17:46

score 78 · Answer 14 · 2019-10-12 23:25:51

78

Views

End = Aut $\Rightarrow$ algebraic?

Published on 12 Oct 2019 - 23:25

score 31 · Answer 15 · 2019-10-13 22:00:15

31

Views

$k \subseteq K$ be a field extension with $[K:k] = p$ prime, $f(X) \in k[x]$ with $\deg{f(X)} = p + 1$. $f$ has a root in $K$ iff has a root in $k$.

Published on 13 Oct 2019 - 22:00

List Question

If $R/k$ is a ring extension, with $k$ a field, $R$ a integer domain, $[R:k]=n\in\mathbb{N}\implies R$ is a field

$L/k$ and $K/k$ field extensions of $k$ with $[L:k]=m,[K:k]=n, (m,n)=1\implies L\cap K=k$

Galois Group of Ordered Field containing Square Roots

Prime degree extension and polynomial root

$x^5-2x^3+2x-2$ irreducible over $\mathbb{Q}(\sqrt[3]{2})$

$K/k$ field extension, $[K:k]=p$ prime, $f(X)\in [X]$ has degree $p+1$, $f$ has root in $K\iff f$ has root in $k$

How many roots of unity exists in $K=\Bbb Q_2(\sqrt{-3})$

$K/k$ field extension, $[K:k]=n,f(x)\in k[x]$ irreducible over $k$ with degree $m$, and $f$ has a root in $K\implies m$ divides $n$

About the Galois group of the polynomial $f(x)=x^4+ax^2+b$ over $\mathbb Q$

Finding the degree $[\mathbb{Q}(\sqrt[4]{3},\sqrt[5]{3}):\mathbb{Q}]$

Let $F \subseteq E$ be a field extension. Does $F$ isomorphic to $E$ imply $E=F$?

Finding splitting fields over $\mathbb{Q}(\sqrt{-3})$

Must a field extension contain an element of particular degree?

End = Aut $\Rightarrow$ algebraic?

$k \subseteq K$ be a field extension with $[K:k] = p$ prime, $f(X) \in k[x]$ with $\deg{f(X)} = p + 1$. $f$ has a root in $K$ iff has a root in $k$.

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