Question

$x^{2}(x−1)^{2}(x^2+1)+y^2$ is irreducible over $\mathbb{C}[x,y].$

score 70 · Answer 1 · 2026-03-17 10:35:36

70

Views

$x^{2}(x−1)^{2}(x^2+1)+y^2$ is irreducible over $\mathbb{C}[x,y].$

Published on 17 Mar 2026 - 10:35

score 76 · Answer 2 · 2026-03-20 08:13:44

76

Views

Is the following polynomial irreductible over $\mathbb{Z}[X]$?

Published on 20 Mar 2026 - 8:13

score 415 · Answer 3 · 2026-03-22 08:15:24

415

Views

Does irreducibility in $\mathbb{F}_p[x]$ imply irreducibility in $\mathbb{Q}[x]$?

Published on 22 Mar 2026 - 8:15

score 152 · Answer 4 · 2026-03-19 18:25:33

152

Views

discriminant and irreducibility of $x^p - (p+1)x - 1$

Published on 19 Mar 2026 - 18:25

score 303 · Answer 5 · 2026-03-20 06:11:10

303

Views

galois group of irreducible monic cubic polynomial

Published on 20 Mar 2026 - 6:11

score 76 · Answer 6 · 2026-03-22 07:48:33

76

Views

When will $F[x]/\langle p(x)\rangle$ strictly contain $F$?

Published on 22 Mar 2026 - 7:48

score 195 · Answer 7 · 2026-03-20 04:19:07

195

Views

On reducibility over $\mathbb{Z}$ of a special class of polynomials .

Published on 20 Mar 2026 - 4:19

score 89 · Answer 8 · 2026-03-23 03:50:37

89

Views

Eisenstein's criterion over polynomials irreducible

Published on 23 Mar 2026 - 3:50

score 156 · Answer 9 · 2026-03-20 02:32:31

156

Views

Optimal normal basis in Tower field construction

Published on 20 Mar 2026 - 2:32

score 77 · Answer 10 · 2026-03-22 10:22:14

77

Views

If $f$ has $\deg(f)$ distince roots whose order are the same, then is $f$ irreducible?

Published on 22 Mar 2026 - 10:22

score 57 · Answer 11 · 2026-03-22 12:57:01

57

Views

Irreducibility for polynomial in $\mathbb{Z}[i][X]$

Published on 22 Mar 2026 - 12:57

score 196 · Answer 12 · 2026-03-20 09:45:46

196

Views

$f\in K[X]$ irreducible odd degree, $\alpha, \beta\in\bar K$ distinct roots of $f$ $\Rightarrow$ neither $\alpha+\beta\in K$ nor $\alpha\beta\in K$

Published on 20 Mar 2026 - 9:45

score 123 · Answer 13 · 2026-03-17 11:55:41

123

Views

Show that $X^6 - 6125$ is irreducible

Published on 17 Mar 2026 - 11:55

score 118 · Answer 14 · 2026-03-17 11:59:51

118

Views

Can we find an irreducible polynomial of any degree in $\mathbb C[x,y]$?

Published on 17 Mar 2026 - 11:59

score 269 · Answer 15 · 2026-03-17 17:47:37

269

Views

Why is $\mathbb{Q}(\sqrt{2})$ not isomorphic to $\mathbb{Q}(\sqrt{3})$?

Published on 17 Mar 2026 - 17:47

List Question

$x^{2}(x−1)^{2}(x^2+1)+y^2$ is irreducible over $\mathbb{C}[x,y].$

Is the following polynomial irreductible over $\mathbb{Z}[X]$?

Does irreducibility in $\mathbb{F}_p[x]$ imply irreducibility in $\mathbb{Q}[x]$?

discriminant and irreducibility of $x^p - (p+1)x - 1$

galois group of irreducible monic cubic polynomial

When will $F[x]/\langle p(x)\rangle$ strictly contain $F$?

On reducibility over $\mathbb{Z}$ of a special class of polynomials .

Eisenstein's criterion over polynomials irreducible

Optimal normal basis in Tower field construction

If $f$ has $\deg(f)$ distince roots whose order are the same, then is $f$ irreducible?

Irreducibility for polynomial in $\mathbb{Z}[i][X]$

$f\in K[X]$ irreducible odd degree, $\alpha, \beta\in\bar K$ distinct roots of $f$ $\Rightarrow$ neither $\alpha+\beta\in K$ nor $\alpha\beta\in K$

Show that $X^6 - 6125$ is irreducible

Can we find an irreducible polynomial of any degree in $\mathbb C[x,y]$?

Why is $\mathbb{Q}(\sqrt{2})$ not isomorphic to $\mathbb{Q}(\sqrt{3})$?

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