Question

Norm (Number Field) is linear? (Am i making a huge mistake?)

score 47 · Answer 1 · 2026-04-14 03:02:12

47

Views

Norm (Number Field) is linear? (Am i making a huge mistake?)

Published on 14 Apr 2026 - 3:02

score 114 · Answer 2 · 2026-04-15 23:55:24

114

Views

Show: $f=x^p - \alpha$ irreducible and inseparable in field $F(\alpha)$, where $charF=p>0$ and $\alpha$ transcendental over F

Published on 15 Apr 2026 - 23:55

score 108 · Answer 3 · 2026-04-15 21:22:30

108

Views

Quadratic extension $L/K$ is inseparable $\iff$ $char(K)=2$ and $\exists \alpha \in L$ \ $K$ with $\alpha^2 \in K$

Published on 15 Apr 2026 - 21:22

score 62 · Answer 4 · 2026-04-15 20:28:23

62

Views

Is $Gal(K/F)/Gal(K/E)\simeq Gal(E/F)$ true if $K/F,E/F$ are merely normal extensions

Published on 15 Apr 2026 - 20:28

score 120 · Answer 5 · 2026-04-12 21:51:38

120

Views

Degree of a field extension over $\mathbb{C}$

Published on 12 Apr 2026 - 21:51

score 129 · Answer 6 · 2026-04-12 14:23:32

129

Views

Field extension where every intermediate field is Galois-closed

Published on 12 Apr 2026 - 14:23

score 72 · Answer 7 · 2026-04-14 00:24:07

72

Views

field extension is simple

Published on 14 Apr 2026 - 0:24

score 73 · Answer 8 · 2026-04-17 02:24:51

73

Views

Irreductibility of $x^p-t$ for fields $F$ with characteristic $p$ and such that $t$ has not a $p$-root in $F$

Published on 17 Apr 2026 - 2:24

score 65 · Answer 9 · 2026-04-17 12:44:44

65

Views

Over prime fields, are all monic irreducible polynomials primitive?

Published on 17 Apr 2026 - 12:44

score 54 · Answer 10 · 2026-04-12 08:29:49

54

Views

Show for algebraic $L/K$ if $L$ perfect, $K$ not necessarily perfect.

Published on 12 Apr 2026 - 8:29

score 62 · Answer 11 · 2026-04-13 03:11:36

62

Views

Transitivity of discriminant of field extentions

Published on 13 Apr 2026 - 3:11

score 105 · Answer 12 · 2026-04-11 16:48:59

105

Views

Theorem of Hecke on the discriminant of a quadratic field extension

Published on 11 Apr 2026 - 16:48

score 141 · Answer 13 · 2026-04-16 13:55:30

141

Views

I am proposing two conjectures regarding the BCH codes ! Can anybody prove or disprove my conjectures?

Published on 16 Apr 2026 - 13:55

score 98 · Answer 14 · 2026-04-26 02:22:56

98

Views

$[L:K]=2$ and $char(K)\neq 2$ $\Rightarrow$ $L=K(\sqrt{a})$ for an $a \in K$.

Published on 26 Apr 2026 - 2:22

score 156 · Answer 15 · 2026-04-15 19:31:59

156

Views

Splitting field of a degree 3 polynomial is generated by a root and the square root of the discriminant

Published on 15 Apr 2026 - 19:31

List Question

Norm (Number Field) is linear? (Am i making a huge mistake?)

Show: $f=x^p - \alpha$ irreducible and inseparable in field $F(\alpha)$, where $charF=p>0$ and $\alpha$ transcendental over F

Quadratic extension $L/K$ is inseparable $\iff$ $char(K)=2$ and $\exists \alpha \in L$ \ $K$ with $\alpha^2 \in K$

Is $Gal(K/F)/Gal(K/E)\simeq Gal(E/F)$ true if $K/F,E/F$ are merely normal extensions

Degree of a field extension over $\mathbb{C}$

Field extension where every intermediate field is Galois-closed

field extension is simple

Irreductibility of $x^p-t$ for fields $F$ with characteristic $p$ and such that $t$ has not a $p$-root in $F$

Over prime fields, are all monic irreducible polynomials primitive?

Show for algebraic $L/K$ if $L$ perfect, $K$ not necessarily perfect.

Transitivity of discriminant of field extentions

Theorem of Hecke on the discriminant of a quadratic field extension

I am proposing two conjectures regarding the BCH codes ! Can anybody prove or disprove my conjectures?

$[L:K]=2$ and $char(K)\neq 2$ $\Rightarrow$ $L=K(\sqrt{a})$ for an $a \in K$.

Splitting field of a degree 3 polynomial is generated by a root and the square root of the discriminant

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