List questions from irreducible-polynomials

Published on 24 Jun 2020 - 13:35

193

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Let $K = \mathbb{F}_3[T]/(T^3-T+1)$, what would be an irreducible polynomial in $K[X]$ of degree $13$?

Published on 25 Jun 2020 - 11:24

341

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How to calculate the irreducible polynomial in galois field

Published on 26 Jun 2020 - 13:26

75

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Why does the polynomial splitting implies existence primitive root of unity in $\Bbb{F}_{p^2}$?

Published on 27 Jun 2020 - 1:28

140

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Is the ideal $x^3-y^5 \subseteq \mathbb{C}[x,y]$ prime? Is it maximal?

Published on 27 Jun 2020 - 11:01

111

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Basic polynomial questions

Published on 25 Mar 2026 - 19:00

497

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Showing $x^4 + 2$ is irreducible in $F_5[x]$

Published on 29 Jun 2020 - 5:19

154

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Proof? of irreducibility of cyclotomic polynomial

Published on 26 Mar 2026 - 13:01

286

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How to find the generators of the multiplicative group of a finite field

Published on 30 Jun 2020 - 1:59

55

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Points in "general position" with respect to polynomials

Published on 01 Jul 2020 - 16:15

108

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Prove the irreducibility of the polynomial

Published on 03 Jul 2020 - 17:40

33

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Problem with Irreductible Polynomials in $k[x]$, $k$ be an field.

Published on 05 Jul 2020 - 15:53

124

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Relation between irreducible polynomial and dimension

Published on 05 Jul 2020 - 17:46

163

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Let $R=K[x,y,z]/(x^2-yz)$, where $K$ is a field. Show that $R$ is an integral domain, but not a unique factorization domain.

Published on 06 Jul 2020 - 5:44

201

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Proving Irreducibility of $X^{2p}+pX^n-1$ in $\mathbb{Z}[X]$

Published on 06 Jul 2020 - 19:12

List Question

Number of irreducible factors of $x^{p^n + 1} - 1$ over $\Bbb F_p$

Let $K = \mathbb{F}_3[T]/(T^3-T+1)$, what would be an irreducible polynomial in $K[X]$ of degree $13$?

How to calculate the irreducible polynomial in galois field

Why does the polynomial splitting implies existence primitive root of unity in $\Bbb{F}_{p^2}$?

Is the ideal $x^3-y^5 \subseteq \mathbb{C}[x,y]$ prime? Is it maximal?

Basic polynomial questions

Showing $x^4 + 2$ is irreducible in $F_5[x]$

Proof? of irreducibility of cyclotomic polynomial

How to find the generators of the multiplicative group of a finite field

Points in "general position" with respect to polynomials

Prove the irreducibility of the polynomial

Problem with Irreductible Polynomials in $k[x]$, $k$ be an field.

Relation between irreducible polynomial and dimension

Let $R=K[x,y,z]/(x^2-yz)$, where $K$ is a field. Show that $R$ is an integral domain, but not a unique factorization domain.

Proving Irreducibility of $X^{2p}+pX^n-1$ in $\mathbb{Z}[X]$

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