Question

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

score 82 · Answer 1 · 2026-05-05 18:13:01

82

Views

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

Published on 05 May 2026 - 18:13

score 88 · Answer 2 · 2026-05-02 05:11:14

88

Views

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

Published on 02 May 2026 - 5:11

score 423 · Answer 3 · 2026-05-10 13:04:33

423

Views

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

Published on 10 May 2026 - 13:04

score 160 · Answer 4 · 2026-04-29 12:16:35

160

Views

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

Published on 29 Apr 2026 - 12:16

score 312 · Answer 5 · 2026-04-29 12:16:38

312

Views

galois group of irreducible monic cubic polynomial

Published on 29 Apr 2026 - 12:16

score 84 · Answer 6 · 2026-05-10 12:14:48

84

Views

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

Published on 10 May 2026 - 12:14

score 203 · Answer 7 · 2026-04-30 12:33:49

203

Views

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

Published on 30 Apr 2026 - 12:33

score 98 · Answer 8 · 2026-05-03 08:22:06

98

Views

Eisenstein's criterion over polynomials irreducible

Published on 03 May 2026 - 8:22

score 167 · Answer 9 · 2026-05-07 16:52:12

167

Views

Optimal normal basis in Tower field construction

Published on 07 May 2026 - 16:52

score 85 · Answer 10 · 2026-05-04 21:52:22

85

Views

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

Published on 04 May 2026 - 21:52

score 66 · Answer 11 · 2026-05-04 00:56:21

66

Views

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

Published on 04 May 2026 - 0:56

score 203 · Answer 12 · 2026-05-10 11:21:50

203

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 10 May 2026 - 11:21

score 131 · Answer 13 · 2026-05-10 11:20:51

131

Views

Show that $X^6 - 6125$ is irreducible

Published on 10 May 2026 - 11:20

score 125 · Answer 14 · 2026-05-10 11:21:55

125

Views

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

Published on 10 May 2026 - 11:21

score 281 · Answer 15 · 2026-05-10 11:20:04

281

Views

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

Published on 10 May 2026 - 11:20

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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