Question

Construction of a field with roots of unity in MAGMA

score 364 · Answer 1 · 2026-03-25 06:12:48

364

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Construction of a field with roots of unity in MAGMA

Published on 25 Mar 2026 - 6:12

score 67 · Answer 2 · 2026-03-25 23:38:42

67

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Composite of certain Finite Subextensions $L|K$ Galois

Published on 25 Mar 2026 - 23:38

score 77 · Answer 3 · 2026-03-26 14:34:57

77

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degree of extension re: roots of unity to the $2^n$ power and their conjugates

Published on 26 Mar 2026 - 14:34

score 37 · Answer 4 · 2019-03-31 06:10:41

37

Views

Field extensions contradicting tower law

Published on 31 Mar 2019 - 6:10

score 790 · Answer 5 · 2019-03-31 12:05:31

790

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How to show that $\sqrt{2}$ is not in $\mathbb Q(\sqrt{3},\sqrt{5})$?

Published on 31 Mar 2019 - 12:05

score 95 · Answer 6 · 2019-03-31 23:50:14

95

Views

Show that $\mathbb{Q}(\sqrt{1+\sqrt{3}})\cap \mathbb{Q}(\sqrt{1-\sqrt{3}})=\mathbb{Q}(\sqrt{3})$.

Published on 31 Mar 2019 - 23:50

score 336 · Answer 7 · 2019-04-01 01:18:06

336

Views

Tensor Product of Fields is a Field

Published on 01 Apr 2019 - 1:18

score 363 · Answer 8 · 2019-04-01 15:34:02

363

Views

Tensor Product over Algebraically Closed Field

Published on 01 Apr 2019 - 15:34

score 38 · Answer 9 · 2019-04-02 02:57:10

38

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Let $k \subseteq F \subseteq K$ be fields, and let $z \in K$. Prove that if $k(z) \colon k$ is finite, then $[F(z):F] \leq [k(z):k]$.

Published on 02 Apr 2019 - 2:57

score 89 · Answer 10 · 2019-04-03 10:33:20

89

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$[L:K]$ dividing $n!$ with $L=K(\alpha_1,...\alpha_n)$, and $L$ a splitting field of $f$ with $\alpha_1..\alpha_n$ zeros of $f$

Published on 03 Apr 2019 - 10:33

score 139 · Answer 11 · 2019-04-03 16:56:54

With $[K: F] = 3, \alpha \in K, \beta \in K \backslash F$, show that there are $a,b,c,d \in F$ such that $\alpha = \frac{a+b\beta}{c+d\beta}$

score 51 · Answer 12 · 2019-04-03 17:08:24

51

Views

coefficient extension for fraction field $K(T) \otimes_K L$

Published on 03 Apr 2019 - 17:08

score 289 · Answer 13 · 2019-04-03 17:29:55

289

Views

Intersection of Fields

Published on 03 Apr 2019 - 17:29

score 25 · Answer 14 · 2019-04-03 18:32:15

25

Views

Let $K=\mathbb{Q}(\alpha \xi)$. Then choose the correct statements

Published on 03 Apr 2019 - 18:32

score 486 · Answer 15 · 2019-04-05 12:41:13

486

Views

Prove that the Galois Group Is $D_{10}$

Published on 05 Apr 2019 - 12:41

List Question

Construction of a field with roots of unity in MAGMA

Composite of certain Finite Subextensions $L|K$ Galois

degree of extension re: roots of unity to the $2^n$ power and their conjugates

Field extensions contradicting tower law

How to show that $\sqrt{2}$ is not in $\mathbb Q(\sqrt{3},\sqrt{5})$?

Show that $\mathbb{Q}(\sqrt{1+\sqrt{3}})\cap \mathbb{Q}(\sqrt{1-\sqrt{3}})=\mathbb{Q}(\sqrt{3})$.

Tensor Product of Fields is a Field

Tensor Product over Algebraically Closed Field

Let $k \subseteq F \subseteq K$ be fields, and let $z \in K$. Prove that if $k(z) \colon k$ is finite, then $[F(z):F] \leq [k(z):k]$.

$[L:K]$ dividing $n!$ with $L=K(\alpha_1,...\alpha_n)$, and $L$ a splitting field of $f$ with $\alpha_1..\alpha_n$ zeros of $f$

With $[K: F] = 3, \alpha \in K, \beta \in K \backslash F$, show that there are $a,b,c,d \in F$ such that $\alpha = \frac{a+b\beta}{c+d\beta}$

coefficient extension for fraction field $K(T) \otimes_K L$

Intersection of Fields

Let $K=\mathbb{Q}(\alpha \xi)$. Then choose the correct statements

Prove that the Galois Group Is $D_{10}$

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