List questions from field-theory

Published on 14 Apr 2026 - 22:33

277

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Degree of the extension $\mathbb{Q}(\zeta_3,\zeta_7)$ over $\mathbb{Q}$

Published on 15 Apr 2026 - 16:49

8.5k

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Is $\mathbb Q(\sqrt{2},\sqrt{3},\sqrt{5})=\mathbb Q(\sqrt{2}+\sqrt{3}+\sqrt{5})$.

Published on 17 Apr 2026 - 3:25

104

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Show that $x^4+n(2-n)x^2+n^2$ reducible over Q for any natural number n.

Published on 15 Apr 2026 - 22:09

1k

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Find all the fields between $\mathbb{Q}$ and the splitting field of $x^4 + 81$

Published on 15 Apr 2026 - 12:08

951

Views

Field extensions with(out) a common extension

Published on 12 Apr 2026 - 3:22

93

Views

Factorize $x^4+n(2-n)x^2+n^2$ into irreducible polynomials over Q for any natural number n.

Published on 15 Apr 2026 - 13:23

93

Views

Intermediate fields of $X^p - 2 $

Published on 14 Apr 2026 - 17:19

900

Views

What is the Characteristic Polynomial of an element over a field in this case?

Published on 14 Apr 2026 - 0:43

133

Views

Prolonging a discrete valuation in Serre's Local Fields?

Published on 14 Apr 2026 - 0:22

225

Views

What is a system of representatives of the residue field in its ring R?

Published on 12 Apr 2026 - 0:02

1.2k

Views

Are there fields and ordered fields of every infinite cardinality?

Published on 13 Apr 2026 - 9:36

831

Views

Automorphisms of $\mathbb{C}(X)$ and their fixed field

Published on 10 Apr 2026 - 18:25

597

Views

why similarity over $\bar{\mathbb{F}}$ of $A,B\in M_n(\mathbb{F})$ implies similarity over $\mathbb{F}$?

Published on 11 May 2026 - 4:40

200

Views

Field Characteristic Is Prime...?

Published on 12 Apr 2026 - 13:24

List Question

Find extension degree

Degree of the extension $\mathbb{Q}(\zeta_3,\zeta_7)$ over $\mathbb{Q}$

Is $\mathbb Q(\sqrt{2},\sqrt{3},\sqrt{5})=\mathbb Q(\sqrt{2}+\sqrt{3}+\sqrt{5})$.

Show that $x^4+n(2-n)x^2+n^2$ reducible over Q for any natural number n.

Find all the fields between $\mathbb{Q}$ and the splitting field of $x^4 + 81$

Field extensions with(out) a common extension

Factorize $x^4+n(2-n)x^2+n^2$ into irreducible polynomials over Q for any natural number n.

Intermediate fields of $X^p - 2 $

What is the Characteristic Polynomial of an element over a field in this case?

Prolonging a discrete valuation in Serre's Local Fields?

What is a system of representatives of the residue field in its ring R?

Are there fields and ordered fields of every infinite cardinality?

Automorphisms of $\mathbb{C}(X)$ and their fixed field

why similarity over $\bar{\mathbb{F}}$ of $A,B\in M_n(\mathbb{F})$ implies similarity over $\mathbb{F}$?

Field Characteristic Is Prime...?

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