Question

Existence of algebraically closed and algebraic field over another field

score 136 · Answer 1 · 2019-02-07 17:33:34

136

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Existence of algebraically closed and algebraic field over another field

Published on 07 Feb 2019 - 17:33

score 146 · Answer 2 · 2026-03-26 22:14:51

146

Views

Do the trace and norm always belong to the base field?

Published on 26 Mar 2026 - 22:14

score 86 · Answer 3 · 2026-03-25 19:25:20

86

Views

Find the splitting field $K$ of $x^{12}-9$ over $\mathbb{Q}$ and determine $[K:\mathbb{Q}]$.

Published on 25 Mar 2026 - 19:25

score 78 · Answer 4 · 2026-04-04 00:43:42

78

Views

Determine $[\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11}):\mathbb{Q}]$, and determine if $\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11})/\mathbb{Q}$ is normal

Published on 04 Apr 2026 - 0:43

score 189 · Answer 5 · 2026-03-31 08:01:18

189

Views

If $K/F$ is normal extension, $I$ is inseparable closure of $F$ in $K$, prove $K/I$ is Galois.

Published on 31 Mar 2026 - 8:01

score 139 · Answer 6 · 2026-03-30 14:40:42

139

Views

Transcendental Extension and Algebraic Extension commute.

Published on 30 Mar 2026 - 14:40

score 41 · Answer 7 · 2019-02-08 15:06:44

41

Views

Arithmetic of the field $\mathbb{Q}(\alpha)$

Published on 08 Feb 2019 - 15:06

score 249 · Answer 8 · 2026-03-25 13:34:22

249

Views

Prove that a primitive $q$-th root of unity is in the algebraic closure of $\Bbb F_p$

Published on 25 Mar 2026 - 13:34

score 175 · Answer 9 · 2026-03-25 06:06:38

175

Views

Lang's Algebra: definition of $F[\alpha]$ and why it's an integral domain?

Published on 25 Mar 2026 - 6:06

score 32 · Answer 10 · 2019-02-08 20:07:17

32

Views

Difficulties with the definition of extension

Published on 08 Feb 2019 - 20:07

score 1.6k · Answer 11 · 2019-02-09 07:32:35

1.6k

Views

Does every complete ordered field $ \mathbb{F}$ hold the Archimedean property?

Published on 09 Feb 2019 - 7:32

score 91 · Answer 12 · 2026-03-25 09:37:03

91

Views

Application Nakayama's Lemma for Field Extensions $L \vert K$

Published on 25 Mar 2026 - 9:37

score 141 · Answer 13 · 2019-02-10 11:38:07

141

Views

Cardinality of subfields of real numbers

Published on 10 Feb 2019 - 11:38

score 74 · Answer 14 · 2026-03-25 07:40:51

74

Views

Showing this is an automorphism

Published on 25 Mar 2026 - 7:40

score 235 · Answer 15 · 2026-03-30 14:36:41

235

Views

Pythagorean closure

Published on 30 Mar 2026 - 14:36

List Question

Existence of algebraically closed and algebraic field over another field

Do the trace and norm always belong to the base field?

Find the splitting field $K$ of $x^{12}-9$ over $\mathbb{Q}$ and determine $[K:\mathbb{Q}]$.

Determine $[\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11}):\mathbb{Q}]$, and determine if $\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11})/\mathbb{Q}$ is normal

If $K/F$ is normal extension, $I$ is inseparable closure of $F$ in $K$, prove $K/I$ is Galois.

Transcendental Extension and Algebraic Extension commute.

Arithmetic of the field $\mathbb{Q}(\alpha)$

Prove that a primitive $q$-th root of unity is in the algebraic closure of $\Bbb F_p$

Lang's Algebra: definition of $F[\alpha]$ and why it's an integral domain?

Difficulties with the definition of extension

Does every complete ordered field $ \mathbb{F}$ hold the Archimedean property?

Application Nakayama's Lemma for Field Extensions $L \vert K$

Cardinality of subfields of real numbers

Showing this is an automorphism

Pythagorean closure

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