List questions from extension-field

Published on 10 Jun 2015 - 10:06

2.5k

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Galois group of primitive root of unity/ field extensions

Published on 10 Apr 2026 - 21:56

397

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finding intermediate fields of field extensions: simple method vs. Galois theory

Published on 11 Apr 2026 - 22:39

1.4k

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Showing that $\mathbb{Q}\left(\sqrt{2},\sqrt{3}, \sqrt{(9 - 5\sqrt{3})(2-\sqrt{2})}\right)$ is normal over $\mathbb{Q}$, and finding its Galois group

Published on 10 Jun 2015 - 21:36

137

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looking for the inverse of $3+2\alpha^2$ over $\Bbb Q(\alpha)$ with $\alpha=\sqrt[3]{2}$

Published on 11 Jun 2015 - 10:50

474

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Find and show primitive element of field extension

Published on 14 Jun 2015 - 14:39

2.6k

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Field extension of prime degree

Published on 11 Apr 2026 - 13:24

22

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Splitting of primes terminology doubt

Published on 16 Jun 2015 - 5:54

563

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Cyclic extension without primitive root of unity

Published on 11 Apr 2026 - 10:22

980

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Why is this Galois group abelian?

Published on 18 Jun 2015 - 14:44

137

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How (possibly) many subfields does $\mathbb{F}$ has that extend $\mathbb{Q}$?

Published on 19 Jun 2015 - 7:42

538

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How does one construct the Galois field extension $GF((2^2)^3)$?

Published on 08 Apr 2026 - 5:47

1.9k

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Number of Galois conjugates

Published on 22 Jun 2015 - 15:52

78

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Exercise about cyclic field extension

Published on 22 Jun 2015 - 21:15

969

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Why is is $K(\alpha,\beta)/K(\alpha)$ algebraic if $K(\alpha,\beta)/K(\beta)$ is algebraic?

Published on 23 Jun 2015 - 23:44

List Question

Basis of $\mathbb{Q}[\sqrt[3]{2}]$

Galois group of primitive root of unity/ field extensions

finding intermediate fields of field extensions: simple method vs. Galois theory

Showing that $\mathbb{Q}\left(\sqrt{2},\sqrt{3}, \sqrt{(9 - 5\sqrt{3})(2-\sqrt{2})}\right)$ is normal over $\mathbb{Q}$, and finding its Galois group

looking for the inverse of $3+2\alpha^2$ over $\Bbb Q(\alpha)$ with $\alpha=\sqrt[3]{2}$

Find and show primitive element of field extension

Field extension of prime degree

Splitting of primes terminology doubt

Cyclic extension without primitive root of unity

Why is this Galois group abelian?

How (possibly) many subfields does $\mathbb{F}$ has that extend $\mathbb{Q}$?

How does one construct the Galois field extension $GF((2^2)^3)$?

Number of Galois conjugates

Exercise about cyclic field extension

Why is is $K(\alpha,\beta)/K(\alpha)$ algebraic if $K(\alpha,\beta)/K(\beta)$ is algebraic?

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