List questions from irreducible-polynomials

Published on 19 Jun 2015 - 17:11

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Abstract algebra. Proof of: Let $F$ be a finite field and $P$ an irreducible polynomial upon $F$. Then $(F[t]|_{\equiv_P}, + , \ast)$ is a field.

Published on 19 Jun 2015 - 19:48

361

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Irreducible polynomial modulo 2

Published on 22 Jun 2015 - 21:50

1.7k

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Showing a polynomial is irreducible over $\mathbb{C}[x,y]$

Published on 23 Jun 2015 - 5:11

2.5k

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Show that $\mathbb{Q}(\sqrt{5}+\sqrt[3]{2})=\mathbb{Q}(\sqrt{5},\sqrt[3]{2})$.

Published on 24 Jun 2015 - 1:53

199

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Show that the ideal $I=\left\langle x_1^2+1,x_2,...,x_n\right\rangle$ is maximal in $\mathbb{R}[x_1,...,x_n]$.

Published on 26 Jun 2015 - 17:32

47

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module isomorphism inbetween two equivalence classes of polynomials

Published on 28 Jun 2015 - 15:42

28.2k

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How can I prove irreducibility of polynomial over a finite field?

Published on 29 Jun 2015 - 16:11

129

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For any field $k$ and $n>0$: $X^n-a\text{ reducible }\ \Leftrightarrow\ a=b^p\ \vee\ a=-4b^4$.

Published on 30 Jun 2015 - 21:56

72

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Can two irreducible polynomials have different powers of the same real number as roots?

Published on 04 Jul 2015 - 23:51

56

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Characteristic is positive and exist polynomial with $g(X^p)=f$

Published on 06 Jul 2015 - 9:51

2.1k

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Every irreducible polynomial f over perfect field F is separable

Published on 06 Jul 2015 - 10:12

637

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Irreducibility of cyclotomic polynomials over number fields

Published on 26 Mar 2026 - 22:52

427

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Count the number of monic irreducible polynomials of degree 12 over $\mathbb F_q$

Published on 07 Jul 2015 - 5:41

6k

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Nature of roots of a biquadratic equation

Published on 08 Jul 2015 - 15:18

List Question

Factor the polynomial

Abstract algebra. Proof of: Let $F$ be a finite field and $P$ an irreducible polynomial upon $F$. Then $(F[t]|_{\equiv_P}, + , \ast)$ is a field.

Irreducible polynomial modulo 2

Showing a polynomial is irreducible over $\mathbb{C}[x,y]$

Show that $\mathbb{Q}(\sqrt{5}+\sqrt[3]{2})=\mathbb{Q}(\sqrt{5},\sqrt[3]{2})$.

Show that the ideal $I=\left\langle x_1^2+1,x_2,...,x_n\right\rangle$ is maximal in $\mathbb{R}[x_1,...,x_n]$.

module isomorphism inbetween two equivalence classes of polynomials

How can I prove irreducibility of polynomial over a finite field?

For any field $k$ and $n>0$: $X^n-a\text{ reducible }\ \Leftrightarrow\ a=b^p\ \vee\ a=-4b^4$.

Can two irreducible polynomials have different powers of the same real number as roots?

Characteristic is positive and exist polynomial with $g(X^p)=f$

Every irreducible polynomial f over perfect field F is separable

Irreducibility of cyclotomic polynomials over number fields

Count the number of monic irreducible polynomials of degree 12 over $\mathbb F_q$

Nature of roots of a biquadratic equation

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