List questions from irreducible-polynomials

Published on 13 May 2018 - 2:11

55

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A minimal polynomial problem that's bothering me

Published on 14 May 2018 - 16:11

304

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Show that Matrix $M$ is diagonizable if the characteristic polynomial is irreducible

Published on 25 Mar 2026 - 5:03

442

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Prove that if $x $ is transcendental over $F $ then $t^2-x \in F (x)[t] $ is irreducible

Published on 16 May 2018 - 4:25

68

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Question about separable polynomial - proof verification

Published on 22 Mar 2026 - 16:57

65

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Irreducibility of polynomial in $\Bbb F_p[x]$

Published on 16 May 2018 - 7:13

94

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primitive polynomials of degree $d$ over $F_{3^3}$

Published on 16 May 2018 - 16:34

52

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Evaluate an expression as an element of $F$

Published on 23 Mar 2026 - 13:40

40

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A question about some polynomial

Published on 18 May 2018 - 10:14

242

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Prove that $m(x)$ is is the minimum polynomial of $\alpha$ over $K$ ff $m(x)$ is irred in $K[x]$

Published on 19 May 2018 - 18:17

28

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A set of generators in disjoint cycle notation. Сompute the Galois group of an irreducible polynomial

Published on 19 May 2018 - 22:25

46

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Does the degree of the splitting field of any irreducible $n$-degree polynomial equal $n$?

Published on 20 May 2018 - 23:33

467

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The Galois group of a specialized polynomial

Published on 23 Mar 2026 - 4:21

1.1k

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Finding an irreducible polynomial of degree $n$ in $\mathbb Q[X]$ with real roots

Published on 25 Mar 2026 - 6:06

173

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$\Bbb F_p(\alpha)\cong\Bbb F_p[x]/(f(x))$

Published on 23 May 2018 - 9:31

List Question

Finding irreducible factors of $f=t^6-3$ for the fields $F = \mathbb{ Q, Z/5Z, Z/7Z}$

A minimal polynomial problem that's bothering me

Show that Matrix $M$ is diagonizable if the characteristic polynomial is irreducible

Prove that if $x $ is transcendental over $F $ then $t^2-x \in F (x)[t] $ is irreducible

Question about separable polynomial - proof verification

Irreducibility of polynomial in $\Bbb F_p[x]$

primitive polynomials of degree $d$ over $F_{3^3}$

Evaluate an expression as an element of $F$

A question about some polynomial

Prove that $m(x)$ is is the minimum polynomial of $\alpha$ over $K$ ff $m(x)$ is irred in $K[x]$

A set of generators in disjoint cycle notation. Сompute the Galois group of an irreducible polynomial

Does the degree of the splitting field of any irreducible $n$-degree polynomial equal $n$?

The Galois group of a specialized polynomial

Finding an irreducible polynomial of degree $n$ in $\mathbb Q[X]$ with real roots

$\Bbb F_p(\alpha)\cong\Bbb F_p[x]/(f(x))$

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