List questions from galois-theory

Published on 25 Oct 2014 - 20:30

56

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Showing an algebraic element of $\bar{\mathbb{Q}}$ is in $\bar{\mathbb{Q}}$

Published on 29 Oct 2014 - 20:40

30

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Prove that if $f\in R[X]$ , then $\displaystyle\prod _{\sigma \in G}f^{\sigma}\in \mathbb{Z}[X].$

Published on 30 Oct 2014 - 11:25

208

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Normal basis theorem

Published on 30 Oct 2014 - 12:59

93

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The galois group of the polynomial $x^9+x^3+1$

Published on 30 Oct 2014 - 18:31

1k

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How is $Gal(\mathbb Q(\sqrt{2+\sqrt{2}})/\mathbb Q)\cong \mathbb Z/4\mathbb Z$?

Published on 31 Mar 2026 - 10:37

637

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Equivalent conditions of a Galois extension (Exercise VI.4 in Lang's Algebra)

Published on 01 Nov 2014 - 6:08

1.6k

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Norm of an element in cyclotomic extension (Exercises VI.19 Lang's Algebra)

Published on 26 Mar 2026 - 6:22

2.6k

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What is the overall idea of Galois theory?

Published on 25 Mar 2026 - 2:31

1.4k

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Embedding of a field in a cyclic extension

Published on 02 Nov 2014 - 19:18

107

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Sppliting field and Galois theory and its Automorphism group

Published on 02 Nov 2014 - 23:10

178

Views

Separable field extensions are Frobenius algebras

Published on 03 Nov 2014 - 3:12

144

Views

Prove that $a$ is a $p$th power in $k$ if only if it is in $K$

Published on 02 Apr 2026 - 17:43

4.4k

Views

Kummer-Dedekind's factorisation theorem

Published on 04 Nov 2014 - 11:43

144

Views

Galois extensions questions

Published on 02 Apr 2026 - 19:11

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how much certain mathematician has been cited in recent articles

Showing an algebraic element of $\bar{\mathbb{Q}}$ is in $\bar{\mathbb{Q}}$

Prove that if $f\in R[X]$ , then $\displaystyle\prod _{\sigma \in G}f^{\sigma}\in \mathbb{Z}[X].$

Normal basis theorem

The galois group of the polynomial $x^9+x^3+1$

How is $Gal(\mathbb Q(\sqrt{2+\sqrt{2}})/\mathbb Q)\cong \mathbb Z/4\mathbb Z$?

Equivalent conditions of a Galois extension (Exercise VI.4 in Lang's Algebra)

Norm of an element in cyclotomic extension (Exercises VI.19 Lang's Algebra)

What is the overall idea of Galois theory?

Embedding of a field in a cyclic extension

Sppliting field and Galois theory and its Automorphism group

Separable field extensions are Frobenius algebras

Prove that $a$ is a $p$th power in $k$ if only if it is in $K$

Kummer-Dedekind's factorisation theorem

Galois extensions questions

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