Question

Irreducibility over $\mathbb{Q}[\sqrt[n]{p}]$

score 245 · Answer 1 · 2026-04-13 19:12:59

245

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Irreducibility over $\mathbb{Q}[\sqrt[n]{p}]$

Published on 13 Apr 2026 - 19:12

score 95 · Answer 2 · 2026-04-13 18:33:04

95

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Generalised Lambert W and irreducible polynomials

Published on 13 Apr 2026 - 18:33

score 65 · Answer 3 · 2026-04-14 04:45:44

65

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Is there a 3rd degree irreducible polynomial over Q[x], such that two of it's roots' (over C[x]) product equals the third root?

Published on 14 Apr 2026 - 4:45

score 46 · Answer 4 · 2026-04-12 20:03:32

How to prove the modular reduction of the coefficients of a polynomials in $\mathbb{Z}$ being irreducible implies irreducibility in $\mathbb{Q}[x]$

score 176 · Answer 5 · 2026-04-15 05:34:04

176

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Prove that $x^2 + \alpha x + {\alpha}^2$ is irreducible over $\Bbb{Q}(\alpha)$ where $\alpha ^3 = 2$.

Published on 15 Apr 2026 - 5:34

score 97 · Answer 6 · 2026-04-12 14:22:59

97

Views

Is every polynomial of even degree reducible after some field extensions of degree 2?

Published on 12 Apr 2026 - 14:22

score 112 · Answer 7 · 2022-11-07 19:35:11

Prove that $x^4 + \alpha x^3 + {\alpha}^2 x^2 + {\alpha}^3 x + {\alpha}^4$ is irreducible over $\Bbb{Q}(\alpha)$ where $\alpha ^5 = 2$.

score 450 · Answer 8 · 2026-04-15 03:46:34

450

Views

Minimal polynomial of $\sqrt{1+\sqrt{2}}$ over $\mathbb{Q}$

Published on 15 Apr 2026 - 3:46

score 139 · Answer 9 · 2026-03-29 18:11:59

139

Views

Monic polynomials with coefficients in a local ring

Published on 29 Mar 2026 - 18:11

score 31 · Answer 10 · 2026-04-14 20:33:35

31

Views

Let $\phi(t)$ an irreductible monic divisor of the characteristic polynomial of T, hence $(\phi(t))^p$ is the T-annihilator of a nonzero vector.

Published on 14 Apr 2026 - 20:33

score 480 · Answer 11 · 2026-04-11 13:03:19

480

Views

Precise examples for the solvable quintic with the "most complexity" of roots

Published on 11 Apr 2026 - 13:03

score 388 · Answer 12 · 2022-11-18 14:57:50

388

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Find the sum of $\sum_{i=1}^{5}x^5_i+\sum_{i=1}^{5}\frac{1}{x^5_i}$

Published on 18 Nov 2022 - 14:57

score 75 · Answer 13 · 2026-04-13 23:17:37

75

Views

Irreducible polynomials and factors

Published on 13 Apr 2026 - 23:17

score 138 · Answer 14 · 2022-11-25 11:29:01

138

Views

Factoring $x^{24}-1$ in $\mathbb{F}_7[x]$

Published on 25 Nov 2022 - 11:29

score 47 · Answer 15 · 2026-04-14 00:14:59

47

Views

If $f(x)$ is reducible over $\mathbb{Q}$ , find all the possible values of $a$.

Published on 14 Apr 2026 - 0:14

List Question

Irreducibility over $\mathbb{Q}[\sqrt[n]{p}]$

Generalised Lambert W and irreducible polynomials

Is there a 3rd degree irreducible polynomial over Q[x], such that two of it's roots' (over C[x]) product equals the third root?

How to prove the modular reduction of the coefficients of a polynomials in $\mathbb{Z}$ being irreducible implies irreducibility in $\mathbb{Q}[x]$

Prove that $x^2 + \alpha x + {\alpha}^2$ is irreducible over $\Bbb{Q}(\alpha)$ where $\alpha ^3 = 2$.

Is every polynomial of even degree reducible after some field extensions of degree 2?

Prove that $x^4 + \alpha x^3 + {\alpha}^2 x^2 + {\alpha}^3 x + {\alpha}^4$ is irreducible over $\Bbb{Q}(\alpha)$ where $\alpha ^5 = 2$.

Minimal polynomial of $\sqrt{1+\sqrt{2}}$ over $\mathbb{Q}$

Monic polynomials with coefficients in a local ring

Let $\phi(t)$ an irreductible monic divisor of the characteristic polynomial of T, hence $(\phi(t))^p$ is the T-annihilator of a nonzero vector.

Precise examples for the solvable quintic with the "most complexity" of roots

Find the sum of $\sum_{i=1}^{5}x^5_i+\sum_{i=1}^{5}\frac{1}{x^5_i}$

Irreducible polynomials and factors

Factoring $x^{24}-1$ in $\mathbb{F}_7[x]$

If $f(x)$ is reducible over $\mathbb{Q}$ , find all the possible values of $a$.

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