Question

Can every nonarchimedean ordered field be embedded in some hyperreal field?

score 103 · Answer 1 · 2026-04-09 06:05:58

103

Views

Can every nonarchimedean ordered field be embedded in some hyperreal field?

Published on 09 Apr 2026 - 6:05

score 120 · Answer 2 · 2026-04-17 04:48:25

120

Views

Galois group of extension $\mathbb{Q}\left(\sqrt{\sqrt{2}+\sqrt{-2}}\,\right)$

Published on 17 Apr 2026 - 4:48

score 50 · Answer 3 · 2026-04-14 02:14:38

50

Views

About reciprocal of algebraically independent sets

Published on 14 Apr 2026 - 2:14

score 481 · Answer 4 · 2026-04-13 16:45:38

481

Views

Every element of the field extension $k(\alpha)$ can be written as a rational function in $\alpha$ with coefficients in $k$?

Published on 13 Apr 2026 - 16:45

score 42 · Answer 5 · 2026-04-12 23:56:14

42

Views

General form of element in $k(\alpha_i)_{i\in I}$, an algebraic extension

Published on 12 Apr 2026 - 23:56

score 812 · Answer 6 · 2026-04-14 07:21:42

812

Views

Minimal Polynomial of $1+i$ over $\Bbb Q$

Published on 14 Apr 2026 - 7:21

score 97 · Answer 7 · 2026-04-17 13:24:24

97

Views

Is $F=\Bbb {Q} (\sqrt 2, \sqrt [3]2, \sqrt [4] 2,...)$ different from $\bar {\Bbb {Q}} $?

Published on 17 Apr 2026 - 13:24

score 83 · Answer 8 · 2026-04-14 23:29:46

83

Views

Is there a field extension $E$ containing $S$ which has finite dimension when considered as a vector space over $S?$

Published on 14 Apr 2026 - 23:29

score 106 · Answer 9 · 2026-04-15 23:46:15

106

Views

Let $F$ be a field, let $E=F(a)$ be a simple extension field of $F$, and let $b\in E-F$. Prove that $a$ is algebraic over $F(b)$.

Published on 15 Apr 2026 - 23:46

score 853 · Answer 10 · 2026-04-17 11:57:13

853

Views

Prove that $\mathbb{Q}(\sqrt{2+\sqrt{2}}) / \mathbb{Q}$ is a normal extension

Published on 17 Apr 2026 - 11:57

score 509 · Answer 11 · 2026-04-15 05:25:47

509

Views

For a non-normal extension, is the Galois action still transitive on roots that are in the extension?

Published on 15 Apr 2026 - 5:25

score 95 · Answer 12 · 2026-04-09 00:52:10

95

Views

An etale algebra must be of finite degree

Published on 09 Apr 2026 - 0:52

score 53 · Answer 13 · 2026-04-16 10:34:58

53

Views

$2D$ extension field of $\Bbb R_{\gt 0}$ (not equal to itself), which is isomorphic to $\Bbb C$

Published on 16 Apr 2026 - 10:34

score 38 · Answer 14 · 2026-04-11 02:55:52

38

Views

Software to solve system equations over finite field extension.

Published on 11 Apr 2026 - 2:55

score 218 · Answer 15 · 2026-04-12 02:47:12

218

Views

Extension degree must be power of prime

Published on 12 Apr 2026 - 2:47

List Question

Can every nonarchimedean ordered field be embedded in some hyperreal field?

Galois group of extension $\mathbb{Q}\left(\sqrt{\sqrt{2}+\sqrt{-2}}\,\right)$

About reciprocal of algebraically independent sets

Every element of the field extension $k(\alpha)$ can be written as a rational function in $\alpha$ with coefficients in $k$?

General form of element in $k(\alpha_i)_{i\in I}$, an algebraic extension

Minimal Polynomial of $1+i$ over $\Bbb Q$

Is $F=\Bbb {Q} (\sqrt 2, \sqrt [3]2, \sqrt [4] 2,...)$ different from $\bar {\Bbb {Q}} $?

Is there a field extension $E$ containing $S$ which has finite dimension when considered as a vector space over $S?$

Let $F$ be a field, let $E=F(a)$ be a simple extension field of $F$, and let $b\in E-F$. Prove that $a$ is algebraic over $F(b)$.

Prove that $\mathbb{Q}(\sqrt{2+\sqrt{2}}) / \mathbb{Q}$ is a normal extension

For a non-normal extension, is the Galois action still transitive on roots that are in the extension?

An etale algebra must be of finite degree

$2D$ extension field of $\Bbb R_{\gt 0}$ (not equal to itself), which is isomorphic to $\Bbb C$

Software to solve system equations over finite field extension.

Extension degree must be power of prime

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