Question

Transitivity Property of Separable Extensions

score 2.3k · Answer 1 · 2026-04-12 09:42:40

2.3k

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Transitivity Property of Separable Extensions

Published on 12 Apr 2026 - 9:42

score 522 · Answer 2 · 2026-04-13 00:22:47

522

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There always exists a subfield of $\mathbb C$ which is a splitting field for $f(x)$ $\in$ $Q[X]$?

Published on 13 Apr 2026 - 0:22

score 656 · Answer 3 · 2026-04-02 05:22:40

656

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Prove that any two bases of a field extension have the same cardinality.

Published on 02 Apr 2026 - 5:22

score 73 · Answer 4 · 2026-04-02 05:25:54

73

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Is the field formed by algebraic elements of an extension field over $F$ isomorphic to $F[t]$?

Published on 02 Apr 2026 - 5:25

score 2.1k · Answer 5 · 2026-04-12 09:21:07

2.1k

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Showing Galois Group is Abelian

Published on 12 Apr 2026 - 9:21

score 151 · Answer 6 · 2026-03-24 23:56:08

151

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Find valuation rings of the function field $k(x,y)/k(xy)$ which do not contain $k[x,y]$.

Published on 24 Mar 2026 - 23:56

score 817 · Answer 7 · 2026-04-02 05:22:39

817

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Finitely many embeddings of a finite extension in an algebraic closure

Published on 02 Apr 2026 - 5:22

score 476 · Answer 8 · 2026-04-02 05:21:48

476

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Non-isomorphic field extensions of $\mathbb{Q}$

Published on 02 Apr 2026 - 5:21

score 78 · Answer 9 · 2026-04-02 05:23:20

78

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Question on a finite field extension of $\mathbb{Q}$

Published on 02 Apr 2026 - 5:23

score 107 · Answer 10 · 2026-04-09 09:00:40

107

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Extending a morphism to a finite algebraic field extension

Published on 09 Apr 2026 - 9:00

score 307 · Answer 11 · 2026-04-11 03:38:04

307

Views

Counting diagonalizable matrices in $\mathcal{M}_{n}(\mathbb{Z}/p\mathbb{Z})$

Published on 11 Apr 2026 - 3:38

score 157 · Answer 12 · 2026-04-04 04:09:51

157

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Why do nth roots (radicals) have closed forms whilst other polynomial roots do not?

Published on 04 Apr 2026 - 4:09

score 928 · Answer 13 · 2026-04-02 07:05:17

928

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Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.

Published on 02 Apr 2026 - 7:05

score 39 · Answer 14 · 2014-08-14 04:03:38

39

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Field theorem: impossible to satisfy three equations simultaneously in an integer field?

Published on 14 Aug 2014 - 4:03

score 3.2k · Answer 15 · 2026-04-02 07:07:44

3.2k

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Suppose that $f(x)$ and $g(x)$ are irreducible over $F$ and that $\deg f(x)$ and $\deg g(x)$ are relatively prime.

Published on 02 Apr 2026 - 7:07

List Question

Transitivity Property of Separable Extensions

There always exists a subfield of $\mathbb C$ which is a splitting field for $f(x)$ $\in$ $Q[X]$?

Prove that any two bases of a field extension have the same cardinality.

Is the field formed by algebraic elements of an extension field over $F$ isomorphic to $F[t]$?

Showing Galois Group is Abelian

Find valuation rings of the function field $k(x,y)/k(xy)$ which do not contain $k[x,y]$.

Finitely many embeddings of a finite extension in an algebraic closure

Non-isomorphic field extensions of $\mathbb{Q}$

Question on a finite field extension of $\mathbb{Q}$

Extending a morphism to a finite algebraic field extension

Counting diagonalizable matrices in $\mathcal{M}_{n}(\mathbb{Z}/p\mathbb{Z})$

Why do nth roots (radicals) have closed forms whilst other polynomial roots do not?

Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.

Field theorem: impossible to satisfy three equations simultaneously in an integer field?

Suppose that $f(x)$ and $g(x)$ are irreducible over $F$ and that $\deg f(x)$ and $\deg g(x)$ are relatively prime.

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