Question

Two irreducible polynomials are equal

score 220 · Answer 1 · 2026-04-10 07:56:09

220

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Two irreducible polynomials are equal

Published on 10 Apr 2026 - 7:56

score 2.4k · Answer 2 · 2026-04-16 08:13:31

2.4k

Views

How to formally prove that a degree 2 or 3 polynomial f(x) ∈ F[x] is irreducible if and only if it has no root in F

Published on 16 Apr 2026 - 8:13

score 331 · Answer 3 · 2026-04-15 22:03:51

331

Views

Are there square integrable vector field solutions of curl(F) = F?

Published on 15 Apr 2026 - 22:03

score 244 · Answer 4 · 2026-04-12 04:00:52

244

Views

Polynomial irreducible over an extension with coprime degree.

Published on 12 Apr 2026 - 4:00

score 78 · Answer 5 · 2026-04-16 18:22:46

78

Views

$x+y=x-y$ in $\mathbb F_q$ when $q$ is even.

Published on 16 Apr 2026 - 18:22

score 25 · Answer 6 · 2026-04-16 16:19:45

25

Views

Proving that $\Bbb{Q}(\xi^2 2^{2/5}+\xi^3 2^{3/5})=\Bbb{Q}(\xi2^{1/5})$

Published on 16 Apr 2026 - 16:19

score 225 · Answer 7 · 2026-04-13 19:40:04

225

Views

Degree of a field extension over $\mathbb{Q}$

Published on 13 Apr 2026 - 19:40

score 179 · Answer 8 · 2026-04-13 23:25:05

179

Views

Cardinality of the torsion subgroup of a field.

Published on 13 Apr 2026 - 23:25

score 60 · Answer 9 · 2026-04-12 08:54:21

60

Views

Can basic field theory be transposed over to group theory? (polynomials in a group-only setting)

Published on 12 Apr 2026 - 8:54

score 260 · Answer 10 · 2026-04-14 22:25:26

260

Views

Expressing $(\alpha-1)^{-1}$ where $\alpha^3-\alpha^2+\alpha+2=0$

Published on 14 Apr 2026 - 22:25

score 34 · Answer 11 · 2026-04-15 17:19:35

34

Views

Is there a field $K$ and a quadratic polynomial $f\in K[T]$ such that $f^2+1$ is a square in $K[T]$?

Published on 15 Apr 2026 - 17:19

score 27 · Answer 12 · 2026-04-15 09:49:53

27

Views

Does there exist a quadratic polynomial $f \in K(x)[T]$ and $\Delta\in K[x]$ such that $f^2 + \Delta$ and $x^2-1+\Delta$ are both squares

Published on 15 Apr 2026 - 9:49

score 61 · Answer 13 · 2026-04-11 04:26:30

61

Views

An exercise about splitting fields and extensions

Published on 11 Apr 2026 - 4:26

score 212 · Answer 14 · 2026-04-14 00:20:11

212

Views

In any field, does $c$ is a root of a polynomial $ f(x) ∈ F[x]$ implies that $f(x)=(x-c)g(x)$?

Published on 14 Apr 2026 - 0:20

score 198 · Answer 15 · 2026-04-12 14:11:18

198

Views

$A$ valuation ring $\Rightarrow$ $A$-submodules of Frac$(A)$ totally ordered?

Published on 12 Apr 2026 - 14:11

List Question

Two irreducible polynomials are equal

How to formally prove that a degree 2 or 3 polynomial f(x) ∈ F[x] is irreducible if and only if it has no root in F

Are there square integrable vector field solutions of curl(F) = F?

Polynomial irreducible over an extension with coprime degree.

$x+y=x-y$ in $\mathbb F_q$ when $q$ is even.

Proving that $\Bbb{Q}(\xi^2 2^{2/5}+\xi^3 2^{3/5})=\Bbb{Q}(\xi2^{1/5})$

Degree of a field extension over $\mathbb{Q}$

Cardinality of the torsion subgroup of a field.

Can basic field theory be transposed over to group theory? (polynomials in a group-only setting)

Expressing $(\alpha-1)^{-1}$ where $\alpha^3-\alpha^2+\alpha+2=0$

Is there a field $K$ and a quadratic polynomial $f\in K[T]$ such that $f^2+1$ is a square in $K[T]$?

Does there exist a quadratic polynomial $f \in K(x)[T]$ and $\Delta\in K[x]$ such that $f^2 + \Delta$ and $x^2-1+\Delta$ are both squares

An exercise about splitting fields and extensions

In any field, does $c$ is a root of a polynomial $ f(x) ∈ F[x]$ implies that $f(x)=(x-c)g(x)$?

$A$ valuation ring $\Rightarrow$ $A$-submodules of Frac$(A)$ totally ordered?

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