List questions from extension-field

245

Views

Does the data of Galois group, ramified places, and inertia groups, determine a Galois number field?

Published on 16 Jun 2014 - 21:53

140

Views

Galois extension of two fields

Published on 19 Jun 2014 - 11:23

81

Views

Show that a sequence of fields exists

Published on 19 Jun 2014 - 16:23

169

Views

Completion of a metric space vs. field extension

Published on 20 Jun 2014 - 12:48

196

Views

Splitting field and intermediate fields

Published on 21 Jun 2014 - 20:42

44

Views

$[K:F_1]=[K:F_2]$, are $F_1, F_2$ isomorphic?

Published on 23 Jun 2014 - 16:21

606

Views

Question related to integrality of field of fractions

Published on 23 Jun 2014 - 16:49

199

Views

Is $\mathbb{Q}\left( \sqrt[3]{2}, \frac{-1 + i\sqrt{3}}{2}\right):\mathbb{Q}$ a simple extension?

Published on 25 Jun 2014 - 0:06

76

Views

A question about the minimal polynomials of linear transformations in fields.

Published on 27 Jun 2014 - 6:19

1.4k

Views

Embedding Fields in Matrix Rings

Published on 27 Jun 2014 - 12:42

1.1k

Views

Splitting Field of Cubic Polynomial Over the Rationals

Published on 26 Mar 2026 - 6:28

116

Views

If $X^{p^d}\equiv X\text{ mod }f$ for prime numbers $p,d$, then $f\in\mathbb{F}_p[X]$ with $\deg f=d$ is irreducible over $\mathbb{F}_p$

Published on 30 Mar 2026 - 17:09

164

Views

Trascendence of $e^\pi$ and $\pi^e$

Published on 25 Mar 2026 - 23:19

1.3k

Views

Residue field of a local ring as field extension

Published on 27 Mar 2026 - 23:47

76

Views

Integral dependence and field extension

Published on 27 Mar 2026 - 3:50

List Question

Does the data of Galois group, ramified places, and inertia groups, determine a Galois number field?

Galois extension of two fields

Show that a sequence of fields exists

Completion of a metric space vs. field extension

Splitting field and intermediate fields

$[K:F_1]=[K:F_2]$, are $F_1, F_2$ isomorphic?

Question related to integrality of field of fractions

Is $\mathbb{Q}\left( \sqrt[3]{2}, \frac{-1 + i\sqrt{3}}{2}\right):\mathbb{Q}$ a simple extension?

A question about the minimal polynomials of linear transformations in fields.

Embedding Fields in Matrix Rings

Splitting Field of Cubic Polynomial Over the Rationals

If $X^{p^d}\equiv X\text{ mod }f$ for prime numbers $p,d$, then $f\in\mathbb{F}_p[X]$ with $\deg f=d$ is irreducible over $\mathbb{F}_p$

Trascendence of $e^\pi$ and $\pi^e$

Residue field of a local ring as field extension

Integral dependence and field extension

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