Question

Algebraic closure is in some sense minimal

score 118 · Answer 1 · 2026-03-25 11:34:16

118

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Algebraic closure is in some sense minimal

Published on 25 Mar 2026 - 11:34

score 67 · Answer 2 · 2018-05-14 03:04:51

67

Views

How to test if a finite extension contains any zero of an irreducible polynomial?

Published on 14 May 2018 - 3:04

score 767 · Answer 3 · 2018-05-15 13:15:28

767

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Is there a notion of minimal polynomial if the ring is not a field?

Published on 15 May 2018 - 13:15

score 126 · Answer 4 · 2018-05-15 13:44:28

126

Views

Is there a correlation between the degree of an extension and it being an algebraic extension?

Published on 15 May 2018 - 13:44

score 125 · Answer 5 · 2018-05-15 23:39:31

125

Views

degree of $\sqrt{2} + \sqrt[3]{3}$ over $\mathbb Q$

Published on 15 May 2018 - 23:39

score 385 · Answer 6 · 2018-05-16 06:53:32

385

Views

On normal closures of a finite field extension $E/F$

Published on 16 May 2018 - 6:53

score 17 · Answer 7 · 2026-03-16 21:28:06

17

Views

Describe the elemnt in $Q (a^{1/ n}, w) $

Published on 16 Mar 2026 - 21:28

score 467 · Answer 8 · 2018-05-16 18:11:00

467

Views

Show that $K$ can be generated over $F$ by the root of an irreducible quartic polynomial of the form $x^4+bx^2+c$.

Published on 16 May 2018 - 18:11

score 408 · Answer 9 · 2026-03-25 11:25:33

408

Views

Prove that no finite field is algebraically closed (using a particular method)

Published on 25 Mar 2026 - 11:25

score 369 · Answer 10 · 2018-05-17 11:48:22

369

Views

Inverse element in field extension $\mathbb{Q}(\sqrt{2},\sqrt{3})$

Published on 17 May 2018 - 11:48

score 341 · Answer 11 · 2018-05-17 14:12:28

341

Views

Let $w=e^{2\pi i/7}$. Find the lattice of subgroups of Gal$(\mathbb Q(w)/\mathbb Q)$ and of intermediate fields in $\mathbb Q(w)\supseteq\mathbb Q$

Published on 17 May 2018 - 14:12

score 219 · Answer 12 · 2018-05-17 18:21:54

219

Views

Find the Galois group of $\Bbb Q(\zeta_n,\sqrt[n]{2})/\Bbb Q(\zeta_n)$

Published on 17 May 2018 - 18:21

score 59 · Answer 13 · 2026-03-25 11:26:02

59

Views

Calculating the splitting field of this polynomial

Published on 25 Mar 2026 - 11:26

score 726 · Answer 14 · 2018-05-17 20:26:15

726

Views

$K/L$ is normal and $L/F$ is purely inseparable. Show that $K/F$ is normal (Proof verification)

Published on 17 May 2018 - 20:26

score 527 · Answer 15 · 2018-05-17 23:15:31

527

Views

Let $a \in F - F^{p}$. Show that $x^{p} - a$ is irreducible over $F$.

Published on 17 May 2018 - 23:15

List Question

Algebraic closure is in some sense minimal

How to test if a finite extension contains any zero of an irreducible polynomial?

Is there a notion of minimal polynomial if the ring is not a field?

Is there a correlation between the degree of an extension and it being an algebraic extension?

degree of $\sqrt{2} + \sqrt[3]{3}$ over $\mathbb Q$

On normal closures of a finite field extension $E/F$

Describe the elemnt in $Q (a^{1/ n}, w) $

Show that $K$ can be generated over $F$ by the root of an irreducible quartic polynomial of the form $x^4+bx^2+c$.

Prove that no finite field is algebraically closed (using a particular method)

Inverse element in field extension $\mathbb{Q}(\sqrt{2},\sqrt{3})$

Let $w=e^{2\pi i/7}$. Find the lattice of subgroups of Gal$(\mathbb Q(w)/\mathbb Q)$ and of intermediate fields in $\mathbb Q(w)\supseteq\mathbb Q$

Find the Galois group of $\Bbb Q(\zeta_n,\sqrt[n]{2})/\Bbb Q(\zeta_n)$

Calculating the splitting field of this polynomial

$K/L$ is normal and $L/F$ is purely inseparable. Show that $K/F$ is normal (Proof verification)

Let $a \in F - F^{p}$. Show that $x^{p} - a$ is irreducible over $F$.

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