Question

Polynomials of odd degree over $F_{p}$ have a root in $F_{p}$

score 100 · Answer 1 · 2026-04-17 05:20:01

100

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Polynomials of odd degree over $F_{p}$ have a root in $F_{p}$

Published on 17 Apr 2026 - 5:20

score 134 · Answer 2 · 2026-04-13 03:24:21

134

Views

Proving that $2+\sqrt{2}$ is irreducible in $\mathbb{Z}[\sqrt{2}]$.

Published on 13 Apr 2026 - 3:24

score 46 · Answer 3 · 2026-04-16 03:59:03

46

Views

Let $u\in \mathbb{C}$ such that $u^3+2=0$. Is the extension $\mathbb{Q}(u):\mathbb{Q}$ Galois?

Published on 16 Apr 2026 - 3:59

score 133 · Answer 4 · 2026-04-17 12:23:55

133

Views

Find all fields $\mathbb{Q} \subset E \subset \mathbb{Q}(\zeta_{40})$ with $[E:\mathbb{Q}]=2$

Published on 17 Apr 2026 - 12:23

score 87 · Answer 5 · 2026-03-25 22:09:40

87

Views

Why this extension is purely inseparable.

Published on 25 Mar 2026 - 22:09

score 175 · Answer 6 · 2026-04-16 23:00:37

175

Views

Galois group of $X^4 + 20 ∈ ℚ[X]$

Published on 16 Apr 2026 - 23:00

score 823 · Answer 7 · 2026-04-14 05:33:08

823

Views

What can we say about the discriminant of the minimal polynomial of an arbitrary primitive element of a number field?

Published on 14 Apr 2026 - 5:33

score 50 · Answer 8 · 2026-04-12 01:08:52

50

Views

Checking if there is some square root of an element over an extension of the field of 5-adic numbers

Published on 12 Apr 2026 - 1:08

score 43 · Answer 9 · 2026-04-16 08:55:35

Let $ \mathbb{K}$ be a field with 27 elements and $ a \in \mathbb{K}$. Then there exists $ x, y \in \mathbb{K}$ such that $ x^3 + y^5 = a$.

score 166 · Answer 10 · 2026-04-13 08:47:21

166

Views

Normal closure of finite extension

Published on 13 Apr 2026 - 8:47

score 145 · Answer 11 · 2026-04-12 10:46:46

145

Views

Is the sum of two primitive elements primitive?

Published on 12 Apr 2026 - 10:46

score 94 · Answer 12 · 2026-04-16 15:17:21

94

Views

Galois group of $f := X^6 - 6 ∈ \Bbb Q[X]$

Published on 16 Apr 2026 - 15:17

score 47 · Answer 13 · 2026-04-12 19:24:45

47

Views

Is a field of characteristic zero where -1 is a square algebraically closed?

Published on 12 Apr 2026 - 19:24

score 136 · Answer 14 · 2026-04-16 05:52:27

136

Views

Galois group of $f := X^6 - 6 \in \Bbb F_5[X], \Bbb F_7[X]$

Published on 16 Apr 2026 - 5:52

score 173 · Answer 15 · 2026-04-14 16:07:19

173

Views

In an algebraically closed field, does every nonzero element have n distinct n-th roots?

Published on 14 Apr 2026 - 16:07

List Question

Polynomials of odd degree over $F_{p}$ have a root in $F_{p}$

Proving that $2+\sqrt{2}$ is irreducible in $\mathbb{Z}[\sqrt{2}]$.

Let $u\in \mathbb{C}$ such that $u^3+2=0$. Is the extension $\mathbb{Q}(u):\mathbb{Q}$ Galois?

Find all fields $\mathbb{Q} \subset E \subset \mathbb{Q}(\zeta_{40})$ with $[E:\mathbb{Q}]=2$

Why this extension is purely inseparable.

Galois group of $X^4 + 20 ∈ ℚ[X]$

What can we say about the discriminant of the minimal polynomial of an arbitrary primitive element of a number field?

Checking if there is some square root of an element over an extension of the field of 5-adic numbers

Let $ \mathbb{K}$ be a field with 27 elements and $ a \in \mathbb{K}$. Then there exists $ x, y \in \mathbb{K}$ such that $ x^3 + y^5 = a$.

Normal closure of finite extension

Is the sum of two primitive elements primitive?

Galois group of $f := X^6 - 6 ∈ \Bbb Q[X]$

Is a field of characteristic zero where -1 is a square algebraically closed?

Galois group of $f := X^6 - 6 \in \Bbb F_5[X], \Bbb F_7[X]$

In an algebraically closed field, does every nonzero element have n distinct n-th roots?

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