List questions from irreducible-polynomials

Published on 03 Jan 2024 - 12:36

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Irreducible polynomial in Dedekind domain

Published on 09 Jan 2024 - 16:48

92

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Factorize $x^4 + 4x^2 +1$ over $\mathbb{F}_{29}$

Published on 29 Mar 2026 - 3:03

61

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How to prove that this multivariable polynomial quotientring is a field, and to what field is it isomorphic?

Published on 14 Jan 2024 - 17:32

63

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Irreducible polynomials in $\mathbb F_q[T]$

Published on 16 Jan 2024 - 4:55

89

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Is $y^{7}+x^{3}z^{4}-x^{2}yz^{4}$ irreducible in $\mathbb{C}[x,y,z]$?

Published on 18 Jan 2024 - 13:37

66

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Irreducibility of $f$, automorphisms $\sigma \in \text{Aut}_{\mathbb Q}(L)$

Published on 27 Mar 2026 - 15:36

146

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$f(X) = X^9 - 2dX^6 + 3d^2 X^3 - d^3$ irreducible in $\mathbb{Q}[X]$ for given cube-free integer $d>1$.

Published on 19 Jan 2024 - 0:17

61

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Polynomial irreducibility over $\mathbb{Z}_{3}[x]$

Published on 19 Jan 2024 - 10:55

82

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Polynomial factorisation over quotient ring

Published on 19 Jan 2024 - 12:54

99

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Why is this proof wrong, or not preferred?

Published on 22 Jan 2024 - 22:01

28

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"Galois group" acts transitively on irreducible factors in the context of normal extensions (not necessarily separable)

Published on 23 Jan 2024 - 12:41

106

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Find the generator of a cyclic group $(\ ^{\mathbb{Z}_{5}[x]}\!/\!_{(g(x))})^{*}$

Published on 28 Jan 2024 - 20:50

64

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Some examples of the following irreducibility test and its name.

Published on 29 Jan 2024 - 17:53

143

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Is there an algorithm to check if a polynomial with integer coefficients is reducible over some extension of $\mathbb Q$?

Published on 04 Feb 2024 - 23:31

List Question

Is $X^4-3X^2+2X+1$ irreducible over the rationals?

Irreducible polynomial in Dedekind domain

Factorize $x^4 + 4x^2 +1$ over $\mathbb{F}_{29}$

How to prove that this multivariable polynomial quotientring is a field, and to what field is it isomorphic?

Irreducible polynomials in $\mathbb F_q[T]$

Is $y^{7}+x^{3}z^{4}-x^{2}yz^{4}$ irreducible in $\mathbb{C}[x,y,z]$?

Irreducibility of $f$, automorphisms $\sigma \in \text{Aut}_{\mathbb Q}(L)$

$f(X) = X^9 - 2dX^6 + 3d^2 X^3 - d^3$ irreducible in $\mathbb{Q}[X]$ for given cube-free integer $d>1$.

Polynomial irreducibility over $\mathbb{Z}_{3}[x]$

Polynomial factorisation over quotient ring

Why is this proof wrong, or not preferred?

"Galois group" acts transitively on irreducible factors in the context of normal extensions (not necessarily separable)

Find the generator of a cyclic group $(\ ^{\mathbb{Z}_{5}[x]}\!/\!_{(g(x))})^{*}$

Some examples of the following irreducibility test and its name.

Is there an algorithm to check if a polynomial with integer coefficients is reducible over some extension of $\mathbb Q$?

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