List questions from field-theory

Published on 17 Mar 2026 - 21:39

68

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Order of $\mathbb F_q^n$?

Published on 25 Mar 2026 - 9:26

1.3k

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Splitting field for $x^6-4$

Published on 25 Mar 2026 - 9:31

67

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Is there a name for the polynomial $x^n-a$?

Published on 25 Mar 2026 - 17:24

41

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Polynomial in algebraic extension as a factor of a different polynomial

Published on 09 Feb 2018 - 6:27

103

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Degree of extension $[K(\alpha):F(\alpha)]$

Published on 25 Mar 2026 - 3:07

55

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How do I guarantee the existence of a quadratic non-residue in $\mathbb{F}_p$

Published on 25 Mar 2026 - 9:29

38

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Calculating minimum polynomial

Published on 25 Mar 2026 - 2:56

430

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Sanity check regarding Galois group of $X^8 - 3$

Published on 26 Mar 2026 - 14:22

246

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Can an algebraic extension be isomorphic to a proper subfield?

Published on 10 Feb 2018 - 20:51

93

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About splitting fields and primitive elements.

Published on 25 Mar 2026 - 2:56

473

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Help me understand this missing detail: transitivity of the field norm.

Published on 12 Feb 2018 - 3:37

99

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Equivalent definitions of the field norm?

Published on 12 Feb 2018 - 9:42

1.2k

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Let $F[[X]]$ be the ring of formal power series over the field $F$. Show that $(X)$ is a maximal ideal.

Published on 20 Mar 2026 - 0:51

94

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Irreducible Factorization of $x^4 - 1$ over $\mathbb{F_3}$.

Published on 12 Feb 2018 - 16:40

List Question

Using Eisenstein's Criterion on something besides an integer

Order of $\mathbb F_q^n$?

Splitting field for $x^6-4$

Is there a name for the polynomial $x^n-a$?

Polynomial in algebraic extension as a factor of a different polynomial

Degree of extension $[K(\alpha):F(\alpha)]$

How do I guarantee the existence of a quadratic non-residue in $\mathbb{F}_p$

Calculating minimum polynomial

Sanity check regarding Galois group of $X^8 - 3$

Can an algebraic extension be isomorphic to a proper subfield?

About splitting fields and primitive elements.

Help me understand this missing detail: transitivity of the field norm.

Equivalent definitions of the field norm?

Let $F[[X]]$ be the ring of formal power series over the field $F$. Show that $(X)$ is a maximal ideal.

Irreducible Factorization of $x^4 - 1$ over $\mathbb{F_3}$.

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