Question

If $\phi$ is an F-map from $K$ to $E$, both field extensions of $F$, then $\alpha \in K$ and $\phi (\alpha)$ have the same minimum polynomial

score 39 · Answer 1 · 2026-03-31 13:10:24

39

Views

If $\phi$ is an F-map from $K$ to $E$, both field extensions of $F$, then $\alpha \in K$ and $\phi (\alpha)$ have the same minimum polynomial

Published on 31 Mar 2026 - 13:10

score 650 · Answer 2 · 2026-03-25 22:30:52

650

Views

Splitting field of $\sqrt{\vphantom{\sum}1+{\sqrt2}}$ and Galois group

Published on 25 Mar 2026 - 22:30

score 81 · Answer 3 · 2019-04-15 04:15:43

81

Views

Finding primitive element

Published on 15 Apr 2019 - 4:15

score 103 · Answer 4 · 2019-04-15 05:35:03

103

Views

Can radical extension tower of a non-root of unity over $p$-adic fields be Galois?

Published on 15 Apr 2019 - 5:35

score 183 · Answer 5 · 2019-04-15 09:24:14

183

Views

Find prime ideals of Quotient Ring

Published on 15 Apr 2019 - 9:24

score 1.5k · Answer 6 · 2026-04-01 02:03:41

1.5k

Views

Intersection of finite Galois extensions is Galois

Published on 01 Apr 2026 - 2:03

score 49 · Answer 7 · 2026-03-25 03:07:28

49

Views

If $P \in V$ is a polynomial with maximal support $\Sigma$, then $|\Sigma| \geq dim(V)$

Published on 25 Mar 2026 - 3:07

score 87 · Answer 8 · 2026-03-31 15:23:35

87

Views

$\mathbb{Q}(\alpha)\cap\mathbb{R}=\mathbb{Q}$, where $\alpha=\sqrt{\frac{3+\sqrt{7}i}{2}}$

Published on 31 Mar 2026 - 15:23

score 19 · Answer 9 · 2019-04-16 08:38:58

19

Views

Verifying expression, finite fields

Published on 16 Apr 2019 - 8:38

score 2.5k · Answer 10 · 2026-03-28 17:40:17

2.5k

Views

Group of units of a field

Published on 28 Mar 2026 - 17:40

score 120 · Answer 11 · 2026-03-31 15:18:14

120

Views

How to find the basis of an extension field

Published on 31 Mar 2026 - 15:18

score 184 · Answer 12 · 2026-03-31 15:16:58

184

Views

minimal polynomial for $\sqrt{-3}+\sqrt{2}$ over $\mathbb{Q}$

Published on 31 Mar 2026 - 15:16

score 144 · Answer 13 · 2026-03-31 15:24:55

144

Views

Show that there exists an $\alpha \in K$ such that $\alpha^2 \in F$ but $\alpha \notin F$

Published on 31 Mar 2026 - 15:24

score 573 · Answer 14 · 2026-04-01 03:43:25

573

Views

Computing $\phi(\frac32)$ where $\phi$ is an automorphism of $\mathbb Q[\sqrt2]$ such that $\phi(1)=1$ and $\phi(\sqrt2)=\sqrt2$

Published on 01 Apr 2026 - 3:43

score 163 · Answer 15 · 2026-03-28 17:41:58

163

Views

Understanding algebraic closure of finite fields

Published on 28 Mar 2026 - 17:41

List Question

If $\phi$ is an F-map from $K$ to $E$, both field extensions of $F$, then $\alpha \in K$ and $\phi (\alpha)$ have the same minimum polynomial

Splitting field of $\sqrt{\vphantom{\sum}1+{\sqrt2}}$ and Galois group

Finding primitive element

Can radical extension tower of a non-root of unity over $p$-adic fields be Galois?

Find prime ideals of Quotient Ring

Intersection of finite Galois extensions is Galois

If $P \in V$ is a polynomial with maximal support $\Sigma$, then $|\Sigma| \geq dim(V)$

$\mathbb{Q}(\alpha)\cap\mathbb{R}=\mathbb{Q}$, where $\alpha=\sqrt{\frac{3+\sqrt{7}i}{2}}$

Verifying expression, finite fields

Group of units of a field

How to find the basis of an extension field

minimal polynomial for $\sqrt{-3}+\sqrt{2}$ over $\mathbb{Q}$

Show that there exists an $\alpha \in K$ such that $\alpha^2 \in F$ but $\alpha \notin F$

Computing $\phi(\frac32)$ where $\phi$ is an automorphism of $\mathbb Q[\sqrt2]$ such that $\phi(1)=1$ and $\phi(\sqrt2)=\sqrt2$

Understanding algebraic closure of finite fields

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