List questions from irreducible-polynomials

Published on 21 Sep 2016 - 15:23

112

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If $a$ is a zero of $f(x)$ in some extension of $F$, show that $g(x)$ is irreducible over $F(a)$, given $f(x)$ and $g(x)$ are

Published on 24 Sep 2016 - 17:25

278

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Are there irreducible polynomials of "infinite" degree?

Published on 25 Sep 2016 - 23:07

287

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irreducibility of cyclotomic polynomials

Published on 26 Mar 2026 - 10:59

393

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Irreducibility of a polynomial with no roots over $K$, $\mbox{char} K= p$

Published on 29 Sep 2016 - 6:21

76

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Prime ideals of $F[x,y]/(x^2+y^2+1)$, where $F=\mathbb{C}$ or $\mathbb{R}$.

Published on 30 Sep 2016 - 19:13

411

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Ideal of vanishing polynomials associated to an algebraic set generated by a single irreducible polynomial

Published on 01 Oct 2016 - 14:47

754

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Splitting Field Problem

Published on 27 Mar 2026 - 0:33

92

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Is this a correct argument for an irred. polynomial of deg $m$ stays irred. over a field extension of deg $n$ if $n$ and $m$ are co-prime?

Published on 02 Oct 2016 - 9:17

237

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The basic facts about $\mathbb{R}[x,y].$

Published on 28 Mar 2026 - 13:32

44

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How to find irreducible polynomial for Barreto-Naehrig curves?

Published on 06 Oct 2016 - 10:32

152

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Is $f$ a product of two polynomials of degree $2$ over $\Bbb Z$.

Published on 06 Oct 2016 - 17:30

1.8k

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Proving a polynomial is irreducible over a finite field

Published on 07 Oct 2016 - 10:43

53

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To prove an element of $\mathbb{Q}[x]$ is irreducible if it is irreducible in $\mathbb{Z}[x]$

Published on 09 Oct 2016 - 22:52

241

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Polynomial irreducible over an extension with coprime degree.

Published on 10 Oct 2016 - 10:00

List Question

Rabin test to prove poly is irreducible over $\mathbb{F}_2$

If $a$ is a zero of $f(x)$ in some extension of $F$, show that $g(x)$ is irreducible over $F(a)$, given $f(x)$ and $g(x)$ are

Are there irreducible polynomials of "infinite" degree?

irreducibility of cyclotomic polynomials

Irreducibility of a polynomial with no roots over $K$, $\mbox{char} K= p$

Prime ideals of $F[x,y]/(x^2+y^2+1)$, where $F=\mathbb{C}$ or $\mathbb{R}$.

Ideal of vanishing polynomials associated to an algebraic set generated by a single irreducible polynomial

Splitting Field Problem

Is this a correct argument for an irred. polynomial of deg $m$ stays irred. over a field extension of deg $n$ if $n$ and $m$ are co-prime?

The basic facts about $\mathbb{R}[x,y].$

How to find irreducible polynomial for Barreto-Naehrig curves?

Is $f$ a product of two polynomials of degree $2$ over $\Bbb Z$.

Proving a polynomial is irreducible over a finite field

To prove an element of $\mathbb{Q}[x]$ is irreducible if it is irreducible in $\mathbb{Z}[x]$

Polynomial irreducible over an extension with coprime degree.

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