Question

Ideal Class Group of $\mathbb{Q}(\sqrt{65})$

score 955 · Answer 1 · 2026-03-25 06:11:03

955

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Ideal Class Group of $\mathbb{Q}(\sqrt{65})$

Published on 25 Mar 2026 - 6:11

score 326 · Answer 2 · 2018-05-07 13:25:09

326

Views

Can the skew field of quaternions be seen as an extension over $\Bbb C$

Published on 07 May 2018 - 13:25

score 354 · Answer 3 · 2018-05-07 20:09:47

354

Views

Given a field, the field of algebraic elements over it in an algebraically closed field extension is again algebraically closed?

Published on 07 May 2018 - 20:09

score 63 · Answer 4 · 2026-03-25 08:08:56

63

Views

Irreducibility of $X^p -p$

Published on 25 Mar 2026 - 8:08

score 59 · Answer 5 · 2026-03-25 08:13:37

59

Views

Under what conditions is an irreducible polynomial in $\operatorname{GF}(p^m)$ also irreducible in $\operatorname{GF}(p^n)$?

Published on 25 Mar 2026 - 8:13

score 281 · Answer 6 · 2018-05-10 00:34:16

281

Views

Let $K$ be a field, Splitting field $L$ over $K$ of polynomial $f(x)=x^n-\theta$

Published on 10 May 2018 - 0:34

score 251 · Answer 7 · 2026-03-25 07:45:30

251

Views

Galois group of symmetric polynomial extension

Published on 25 Mar 2026 - 7:45

score 99 · Answer 8 · 2026-03-22 12:58:08

99

Views

$\mathbb F_p(t) \leq L $ a finite extension

Published on 22 Mar 2026 - 12:58

score 48 · Answer 9 · 2018-05-11 01:02:18

48

Views

Suppose that $f(x)$ has a nonreal root. Show that 2 divides $|\operatorname{Gal}(f(x))|$

Published on 11 May 2018 - 1:02

score 118 · Answer 10 · 2018-05-11 04:36:12

118

Views

Problem in understanding a theorem in A book of abstract algebra - Charles C Pinter (Chapter 31)

Published on 11 May 2018 - 4:36

score 58 · Answer 11 · 2018-05-11 13:23:58

58

Views

Let $p$ be a prime that does not divide $m$ and let $\omega$ be a primitive $m$th root of unity over$\mathbb{F}_p$.

Published on 11 May 2018 - 13:23

score 53 · Answer 12 · 2018-05-12 10:24:14

53

Views

Let $F$ be a field and $E = F(α)$ where $α^2 ∈ F$ and $α \notin F$. Determine the set $S := \lbrace β ∈ E|β^2 ∈ F\rbrace$

Published on 12 May 2018 - 10:24

score 691 · Answer 13 · 2026-03-20 02:38:31

691

Views

Suppose $K/F $ is finite with $K = F (K^p) $. If a finite set $S $ is linearly independent, prove that so is $S^p $.

Published on 20 Mar 2026 - 2:38

score 125 · Answer 14 · 2026-03-24 23:44:55

125

Views

Cubic cyclic field families

Published on 24 Mar 2026 - 23:44

score 343 · Answer 15 · 2026-03-25 02:29:09

343

Views

if the tensor product of a finite field extension and the separable closure over base field is a field, then their intersection is the base field

Published on 25 Mar 2026 - 2:29

List Question

Ideal Class Group of $\mathbb{Q}(\sqrt{65})$

Can the skew field of quaternions be seen as an extension over $\Bbb C$

Given a field, the field of algebraic elements over it in an algebraically closed field extension is again algebraically closed?

Irreducibility of $X^p -p$

Under what conditions is an irreducible polynomial in $\operatorname{GF}(p^m)$ also irreducible in $\operatorname{GF}(p^n)$?

Let $K$ be a field, Splitting field $L$ over $K$ of polynomial $f(x)=x^n-\theta$

Galois group of symmetric polynomial extension

$\mathbb F_p(t) \leq L $ a finite extension

Suppose that $f(x)$ has a nonreal root. Show that 2 divides $|\operatorname{Gal}(f(x))|$

Problem in understanding a theorem in A book of abstract algebra - Charles C Pinter (Chapter 31)

Let $p$ be a prime that does not divide $m$ and let $\omega$ be a primitive $m$th root of unity over$\mathbb{F}_p$.

Let $F$ be a field and $E = F(α)$ where $α^2 ∈ F$ and $α \notin F$. Determine the set $S := \lbrace β ∈ E|β^2 ∈ F\rbrace$

Suppose $K/F $ is finite with $K = F (K^p) $. If a finite set $S $ is linearly independent, prove that so is $S^p $.

Cubic cyclic field families

if the tensor product of a finite field extension and the separable closure over base field is a field, then their intersection is the base field

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