Question

Show $\mathbb{Q}(2+\sqrt{5})=\mathbb{Q}(\sqrt{5})$

score 105 · Answer 1 · 2026-04-15 18:29:10

105

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Show $\mathbb{Q}(2+\sqrt{5})=\mathbb{Q}(\sqrt{5})$

Published on 15 Apr 2026 - 18:29

score 587 · Answer 2 · 2026-04-15 20:21:39

587

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To find a maximal ideal in $\Bbb{Z}[\sqrt m]$

Published on 15 Apr 2026 - 20:21

score 292 · Answer 3 · 2026-04-15 04:10:06

Every prime field of finite characteristic $p$ is isomorphic to the field $\mathbb Z_{p}$ of the residue classes of the set of integers modulo $p$.

score 453 · Answer 4 · 2026-04-16 18:52:35

453

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Prove that $[\mathbb{Q}(\sqrt[r]{p_1},\cdots ,\sqrt[r]{p_n}):\mathbb{Q}]=r^n$

Published on 16 Apr 2026 - 18:52

score 66 · Answer 5 · 2026-04-14 21:01:50

66

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$|\bar{F}:F|=\infty$ implies that the degree of the irreducible polynomials in $F[x]$ is unbounded?

Published on 14 Apr 2026 - 21:01

score 68 · Answer 6 · 2026-04-14 03:06:52

68

Views

Quicker way of finding minimal polynomial over Q than solving systems of equations?

Published on 14 Apr 2026 - 3:06

score 33 · Answer 7 · 2026-04-12 12:00:35

33

Views

Is this a subgroup of $H$ ?

Published on 12 Apr 2026 - 12:00

score 888 · Answer 8 · 2026-04-10 09:44:04

888

Views

How to find minimal polynomial for finite field

Published on 10 Apr 2026 - 9:44

score 77 · Answer 9 · 2026-04-15 21:53:27

77

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$f\in K[X]\subseteq \mathbb{C}[X]$ with degree $p\geq 5$ irreducible is solvable if and only if $N=K[\alpha_i,\alpha_j]$ for every $i,j$

Published on 15 Apr 2026 - 21:53

score 194 · Answer 10 · 2026-04-16 03:53:17

194

Views

Generalize how many irreducible quadratics are in a finite field of n elements.

Published on 16 Apr 2026 - 3:53

score 47 · Answer 11 · 2026-04-11 05:18:22

47

Views

Invertibility of polynomials

Published on 11 Apr 2026 - 5:18

score 90 · Answer 12 · 2026-04-11 16:35:06

90

Views

Consecutive Galois extensions

Published on 11 Apr 2026 - 16:35

score 141 · Answer 13 · 2026-04-11 03:30:17

141

Views

How do we find polynomial order?

Published on 11 Apr 2026 - 3:30

score 510 · Answer 14 · 2026-04-15 03:52:45

510

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How would you show that $(\mathbb{Q} (\sqrt[3]{2}), +, \cdot)$ is a field? (Linear Algebra)

Published on 15 Apr 2026 - 3:52

score 148 · Answer 15 · 2026-04-16 10:56:08

148

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Understanding the correspondence between $\mathbb{Q}_p^\times$ and $ Gal(\mathbb{Q}_p^{ab}/\mathbb{Q}_p)$

Published on 16 Apr 2026 - 10:56

List Question

Show $\mathbb{Q}(2+\sqrt{5})=\mathbb{Q}(\sqrt{5})$

To find a maximal ideal in $\Bbb{Z}[\sqrt m]$

Every prime field of finite characteristic $p$ is isomorphic to the field $\mathbb Z_{p}$ of the residue classes of the set of integers modulo $p$.

Prove that $[\mathbb{Q}(\sqrt[r]{p_1},\cdots ,\sqrt[r]{p_n}):\mathbb{Q}]=r^n$

$|\bar{F}:F|=\infty$ implies that the degree of the irreducible polynomials in $F[x]$ is unbounded?

Quicker way of finding minimal polynomial over Q than solving systems of equations?

Is this a subgroup of $H$ ?

How to find minimal polynomial for finite field

$f\in K[X]\subseteq \mathbb{C}[X]$ with degree $p\geq 5$ irreducible is solvable if and only if $N=K[\alpha_i,\alpha_j]$ for every $i,j$

Generalize how many irreducible quadratics are in a finite field of n elements.

Invertibility of polynomials

Consecutive Galois extensions

How do we find polynomial order?

How would you show that $(\mathbb{Q} (\sqrt[3]{2}), +, \cdot)$ is a field? (Linear Algebra)

Understanding the correspondence between $\mathbb{Q}_p^\times$ and $ Gal(\mathbb{Q}_p^{ab}/\mathbb{Q}_p)$

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