Question

transcendence degree of the field of generalized power series

score 84 · Answer 1 · 2026-04-12 14:00:10

84

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transcendence degree of the field of generalized power series

Published on 12 Apr 2026 - 14:00

score 122 · Answer 2 · 2026-04-16 07:22:21

122

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$F/K$ field extension, prove if $|E_1:K|$, $|E_2:K|$ are coprime numbers, then $E_1 \cap E_2 = K$

Published on 16 Apr 2026 - 7:22

score 67 · Answer 3 · 2026-04-17 12:22:05

67

Views

$F/K$ finite extension, $p(x)$ irreducible with root in $F$, $\deg(p(x)) \mid [F:K]$?

Published on 17 Apr 2026 - 12:22

score 110 · Answer 4 · 2026-04-15 01:50:15

110

Views

let $k$ be a positive divisor of $q-1$ and $a\in F_q$ be such that the equation $x^k=a$ has no solution in $F_q$...

Published on 15 Apr 2026 - 1:50

score 266 · Answer 5 · 2026-04-14 15:57:35

266

Views

'Simple' Proof: Infinitely Many Galois Fields of Fixed Degree

Published on 14 Apr 2026 - 15:57

score 103 · Answer 6 · 2026-04-17 10:00:09

103

Views

Show that $[\mathbb{F}(a_1,a_2,....a_n):\mathbb{F}]=[\mathbb{F}(a_1):\mathbb{F}].[\mathbb{F}(a_2):\mathbb{F}].......[\mathbb{F}(a_n):\mathbb{F}]$

Published on 17 Apr 2026 - 10:00

score 149 · Answer 7 · 2026-04-17 19:56:47

149

Views

What is the tensor product dependent on the field in an algebra?

Published on 17 Apr 2026 - 19:56

score 28 · Answer 8 · 2026-04-12 07:43:05

28

Views

Does the given inclusion hold?

Published on 12 Apr 2026 - 7:43

score 35 · Answer 9 · 2026-04-11 10:45:05

35

Views

About particular extension field

Published on 11 Apr 2026 - 10:45

score 231 · Answer 10 · 2026-04-16 20:03:21

231

Views

Proving that $\mathbb{Q}[\sqrt{2} + \sqrt{3}] = \mathbb{Q}[\sqrt{2},\sqrt{3}].$

Published on 16 Apr 2026 - 20:03

score 103 · Answer 11 · 2026-04-11 20:38:59

103

Views

Why is this polynomial the minimal?

Published on 11 Apr 2026 - 20:38

score 253 · Answer 12 · 2026-03-25 13:55:38

253

Views

Integer rings and UFDs in transcendental field extensions of $\mathbb{Q}$

Published on 25 Mar 2026 - 13:55

score 90 · Answer 13 · 2026-04-14 07:31:43

90

Views

How to prove that this algebraic field extension is not separable therefore Galois.

Published on 14 Apr 2026 - 7:31

score 276 · Answer 14 · 2026-04-14 21:42:25

276

Views

Find the splitting field of $X^5-11$ over $\mathbb{Q}$ and describe the Galois group of this splitting field over $\mathbb{Q}$

Published on 14 Apr 2026 - 21:42

score 82 · Answer 15 · 2026-04-15 12:12:12

82

Views

Why we need polynomials to prove that $1,a,a^2,\dots , a^{n-1}$ is a field?

Published on 15 Apr 2026 - 12:12

List Question

transcendence degree of the field of generalized power series

$F/K$ field extension, prove if $|E_1:K|$, $|E_2:K|$ are coprime numbers, then $E_1 \cap E_2 = K$

$F/K$ finite extension, $p(x)$ irreducible with root in $F$, $\deg(p(x)) \mid [F:K]$?

let $k$ be a positive divisor of $q-1$ and $a\in F_q$ be such that the equation $x^k=a$ has no solution in $F_q$...

'Simple' Proof: Infinitely Many Galois Fields of Fixed Degree

Show that $[\mathbb{F}(a_1,a_2,....a_n):\mathbb{F}]=[\mathbb{F}(a_1):\mathbb{F}].[\mathbb{F}(a_2):\mathbb{F}].......[\mathbb{F}(a_n):\mathbb{F}]$

What is the tensor product dependent on the field in an algebra?

Does the given inclusion hold?

About particular extension field

Proving that $\mathbb{Q}[\sqrt{2} + \sqrt{3}] = \mathbb{Q}[\sqrt{2},\sqrt{3}].$

Why is this polynomial the minimal?

Integer rings and UFDs in transcendental field extensions of $\mathbb{Q}$

How to prove that this algebraic field extension is not separable therefore Galois.

Find the splitting field of $X^5-11$ over $\mathbb{Q}$ and describe the Galois group of this splitting field over $\mathbb{Q}$

Why we need polynomials to prove that $1,a,a^2,\dots , a^{n-1}$ is a field?

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