Question

On the reducibility of $x^4+ a$ over the rationals

score 81 · Answer 1 · 2020-04-05 01:25:36

81

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On the reducibility of $x^4+ a$ over the rationals

Published on 05 Apr 2020 - 1:25

score 23 · Answer 2 · 2026-02-23 02:40:44

23

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Can we make any conclusion on the numerators of elements in the fraction division ring $D(x)$?

Published on 23 Feb 2026 - 2:40

score 109 · Answer 3 · 2020-04-07 13:29:51

109

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Degrees of the irreducible factors of the polynomial $f = X^p-X+a \in \mathbb{F}_q[X]$.

Published on 07 Apr 2020 - 13:29

score 58 · Answer 4 · 2026-03-26 01:27:06

58

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Irreducible bivariate complex polynomial whose zero-locus contains two given points

Published on 26 Mar 2026 - 1:27

score 182 · Answer 5 · 2026-03-25 08:09:42

182

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On the irreducibility over cyclotomic field in radical extension.

Published on 25 Mar 2026 - 8:09

score 83 · Answer 6 · 2020-04-08 13:31:44

83

Views

Does a polynomial $P(x)$ of degree $n$ over $\mathbb{F_q}$ which satisfy $P(x)|x^{l}-1$ only for $l\ge q^n-1$ is irreducible?

Published on 08 Apr 2020 - 13:31

score 70 · Answer 7 · 2020-04-08 23:11:39

70

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How to verify that a polynomial is reducible and how to find its factors?

Published on 08 Apr 2020 - 23:11

score 42 · Answer 8 · 2020-04-10 13:36:16

42

Views

Can a bivariate polynomial with only algebraic coefficients have monic polynomial factors with non-algebraic coefficients?

Published on 10 Apr 2020 - 13:36

score 570 · Answer 9 · 2020-04-14 11:15:45

570

Views

A polynomial with integer coefficients is irreducible over $\mathbb{Z}$ if and only if it is irreducible over $\mathbb{Q}$

Published on 14 Apr 2020 - 11:15

score 401 · Answer 10 · 2020-04-14 23:30:40

401

Views

Intersection of the zero sets of two multivariate polynomials

Published on 14 Apr 2020 - 23:30

score 130 · Answer 11 · 2020-04-16 15:13:13

130

Views

Is the polynomial $4x^3 - 3x - 1/2 $ irreducible over $\mathbb{Q}$?

Published on 16 Apr 2020 - 15:13

score 234 · Answer 12 · 2020-04-17 07:47:42

234

Views

Irreducibility of a family of polynomials

Published on 17 Apr 2020 - 7:47

score 172 · Answer 13 · 2020-04-18 14:38:26

172

Views

Finding irreducible polynomial for isomorphism

Published on 18 Apr 2020 - 14:38

score 74 · Answer 14 · 2026-03-28 14:44:23

74

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Show $\mathbb Q(u,i)\neq\mathbb Q(u)$ where $u$ is a root of $t^4-3t^2+4$

Published on 28 Mar 2026 - 14:44

score 122 · Answer 15 · 2026-03-26 00:53:31

122

Views

Primitive roots as linear combination of a $\mathbb{Q}$-basis of $\mathbb{Q}(\epsilon)$

Published on 26 Mar 2026 - 0:53

List Question

On the reducibility of $x^4+ a$ over the rationals

Can we make any conclusion on the numerators of elements in the fraction division ring $D(x)$?

Degrees of the irreducible factors of the polynomial $f = X^p-X+a \in \mathbb{F}_q[X]$.

Irreducible bivariate complex polynomial whose zero-locus contains two given points

On the irreducibility over cyclotomic field in radical extension.

Does a polynomial $P(x)$ of degree $n$ over $\mathbb{F_q}$ which satisfy $P(x)|x^{l}-1$ only for $l\ge q^n-1$ is irreducible?

How to verify that a polynomial is reducible and how to find its factors?

Can a bivariate polynomial with only algebraic coefficients have monic polynomial factors with non-algebraic coefficients?

A polynomial with integer coefficients is irreducible over $\mathbb{Z}$ if and only if it is irreducible over $\mathbb{Q}$

Intersection of the zero sets of two multivariate polynomials

Is the polynomial $4x^3 - 3x - 1/2 $ irreducible over $\mathbb{Q}$?

Irreducibility of a family of polynomials

Finding irreducible polynomial for isomorphism

Show $\mathbb Q(u,i)\neq\mathbb Q(u)$ where $u$ is a root of $t^4-3t^2+4$

Primitive roots as linear combination of a $\mathbb{Q}$-basis of $\mathbb{Q}(\epsilon)$

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