List questions from irreducible-polynomials

Published on 25 Mar 2017 - 13:20

299

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How to determine $[\Bbb Q(\sqrt2,\sqrt{-3}):\Bbb Q]$ and $[\Bbb Q(\sqrt[3]2,\zeta_3\sqrt[3]{2}):\Bbb Q]$?

Published on 25 Mar 2017 - 16:18

1.1k

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How to prove that the polynomial $x^3-5$ is irreducible over $\Bbb Q(\sqrt2)$?

Published on 26 Mar 2017 - 2:03

683

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Find the minimal polynomial of $\alpha^2+1$ over $\Bbb F_2$

Published on 26 Mar 2017 - 4:36

180

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Find the minimal polynomial of $i\sqrt{-1+2\sqrt3} \in \Bbb C$ over $\Bbb R$

Published on 26 Mar 2017 - 5:59

453

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Prove that a polynomial is irreducible over $F_{13}$

Published on 28 Mar 2017 - 21:35

128

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Is this polynomial in a finite field irreducible?

Published on 29 Mar 2017 - 9:16

980

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Irreducible polynomials over GF(2) of degree m divide this?

Published on 29 Mar 2017 - 13:49

3k

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roots of polynomial over finite field

Published on 30 Mar 2017 - 11:22

504

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How to find the irreducible polynomial in Q[ζ3]?

Published on 30 Mar 2017 - 12:33

50

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Is there a proof of the irreducibility without comparing coefficients?

Published on 30 Mar 2017 - 20:01

226

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Prove $f$ is irreducible if and only if $f=x-\alpha$ in algebraic closed field

Published on 31 Mar 2017 - 10:12

34

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Is determing whether a polynomial is irreducible easier if all coefficients are non-negative?

Published on 01 Apr 2017 - 9:35

2.7k

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Simple extension of $\mathbb{Q} (\sqrt[4]{2},i)$

Published on 07 Apr 2017 - 1:38

152

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How many roots does one add when considering the quotient of a polynomial ring?

Published on 09 Apr 2017 - 10:23

List Question

Prove that the polynomial $x^3+7x+3$ and $x^3+7x+4$ are irreducible over $\Bbb Q.$

How to determine $[\Bbb Q(\sqrt2,\sqrt{-3}):\Bbb Q]$ and $[\Bbb Q(\sqrt[3]2,\zeta_3\sqrt[3]{2}):\Bbb Q]$?

How to prove that the polynomial $x^3-5$ is irreducible over $\Bbb Q(\sqrt2)$?

Find the minimal polynomial of $\alpha^2+1$ over $\Bbb F_2$

Find the minimal polynomial of $i\sqrt{-1+2\sqrt3} \in \Bbb C$ over $\Bbb R$

Prove that a polynomial is irreducible over $F_{13}$

Is this polynomial in a finite field irreducible?

Irreducible polynomials over GF(2) of degree m divide this?

roots of polynomial over finite field

How to find the irreducible polynomial in Q[ζ3]?

Is there a proof of the irreducibility without comparing coefficients?

Prove $f$ is irreducible if and only if $f=x-\alpha$ in algebraic closed field

Is determing whether a polynomial is irreducible easier if all coefficients are non-negative?

Simple extension of $\mathbb{Q} (\sqrt[4]{2},i)$

How many roots does one add when considering the quotient of a polynomial ring?

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