Question

Square roots of root-expressions: distinguishing quartic Galois groups from copies of $C_4$ or of $D_4$ - exercise M.11, Ch.16 Artin's algebra

score 55 · Answer 1 · 2026-04-17 01:38:40

55

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Square roots of root-expressions: distinguishing quartic Galois groups from copies of $C_4$ or of $D_4$ - exercise M.11, Ch.16 Artin's algebra

Published on 17 Apr 2026 - 1:38

score 104 · Answer 2 · 2026-04-09 13:51:16

104

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Understanding the Galois Extension

Published on 09 Apr 2026 - 13:51

score 128 · Answer 3 · 2026-04-15 01:51:42

128

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Understanding $[\mathbb{K}:\mathbb{F}]$ and other relevant concepts

Published on 15 Apr 2026 - 1:51

score 84 · Answer 4 · 2026-04-12 04:54:19

84

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Can the Rational Numbers be extended to "infinite" Numbers?

Published on 12 Apr 2026 - 4:54

score 304 · Answer 5 · 2026-04-15 01:30:41

304

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Classification of degree $p$ field extensions of characteristic $p$ fields: the non-normal but separable case

Published on 15 Apr 2026 - 1:30

score 262 · Answer 6 · 2026-04-12 19:21:28

262

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Understanding the field extension diagram of $x^3-2$

Published on 12 Apr 2026 - 19:21

score 64 · Answer 7 · 2026-04-11 17:33:25

64

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About the degree of a field extension of the field of rational functions

Published on 11 Apr 2026 - 17:33

score 158 · Answer 8 · 2026-03-25 19:01:28

158

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What is the “maximal hyperreal field”?

Published on 25 Mar 2026 - 19:01

score 48 · Answer 9 · 2026-04-16 07:50:57

48

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Constructing intersections in a regular polygon

Published on 16 Apr 2026 - 7:50

score 59 · Answer 10 · 2026-04-16 19:39:57

59

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Is $\sqrt{3}\notin\mathbb{Q}(\sqrt[4]{2})$ enough to show that $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}(\sqrt[4]{2})]=2$?

Published on 16 Apr 2026 - 19:39

score 34 · Answer 11 · 2026-04-16 17:32:45

34

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Given a finite field of primer order and a certain degree extension, how one finds the "best" irreducible polynomial in terms of computability?

Published on 16 Apr 2026 - 17:32

score 180 · Answer 12 · 2026-04-17 11:08:10

180

Views

Show that $x^{12} - 18x^6 + 82$ is irreducible over $\mathbb{F}_p$

Published on 17 Apr 2026 - 11:08

score 53 · Answer 13 · 2026-03-25 13:55:19

53

Views

Formal completion of a scalar extension

Published on 25 Mar 2026 - 13:55

score 92 · Answer 14 · 2026-04-15 17:28:53

92

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Why do we have that for example $\Bbb Q(\sqrt5, \sqrt{11}) = \Bbb Q(\sqrt5)(\sqrt{11})$?

Published on 15 Apr 2026 - 17:28

score 157 · Answer 15 · 2026-04-14 02:56:43

157

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Show that there exists an $F$-isomorphism $\sigma : K \to K$ that takes $g$ to $h$

Published on 14 Apr 2026 - 2:56

List Question

Square roots of root-expressions: distinguishing quartic Galois groups from copies of $C_4$ or of $D_4$ - exercise M.11, Ch.16 Artin's algebra

Understanding the Galois Extension

Understanding $[\mathbb{K}:\mathbb{F}]$ and other relevant concepts

Can the Rational Numbers be extended to "infinite" Numbers?

Classification of degree $p$ field extensions of characteristic $p$ fields: the non-normal but separable case

Understanding the field extension diagram of $x^3-2$

About the degree of a field extension of the field of rational functions

What is the “maximal hyperreal field”?

Constructing intersections in a regular polygon

Is $\sqrt{3}\notin\mathbb{Q}(\sqrt[4]{2})$ enough to show that $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}(\sqrt[4]{2})]=2$?

Given a finite field of primer order and a certain degree extension, how one finds the "best" irreducible polynomial in terms of computability?

Show that $x^{12} - 18x^6 + 82$ is irreducible over $\mathbb{F}_p$

Formal completion of a scalar extension

Why do we have that for example $\Bbb Q(\sqrt5, \sqrt{11}) = \Bbb Q(\sqrt5)(\sqrt{11})$?

Show that there exists an $F$-isomorphism $\sigma : K \to K$ that takes $g$ to $h$

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