Question

Existence of Intermediate field $F$ of $E$ and $G$ such that the $[G: F] < \infty$

score 55 · Answer 1 · 2026-04-15 00:01:11

55

Views

Existence of Intermediate field $F$ of $E$ and $G$ such that the $[G: F] < \infty$

Published on 15 Apr 2026 - 0:01

score 76 · Answer 2 · 2026-04-16 13:20:34

76

Views

Comparison of degrees of field extensions

Published on 16 Apr 2026 - 13:20

score 348 · Answer 3 · 2026-04-16 03:58:47

348

Views

Degree of Extension from $\mathbb{Q}$ to $\mathbb{Q}(i, \sqrt[4]2)$

Published on 16 Apr 2026 - 3:58

score 327 · Answer 4 · 2026-04-09 02:19:17

327

Views

Four dimensional field over complex numbers

Published on 09 Apr 2026 - 2:19

score 29 · Answer 5 · 2026-04-15 15:58:37

29

Views

Intermediate fields $K((K^{1/p^\infty} \cap L)^{p^\infty})$ and $K(K(L^{p^\infty}))^{1/p^\infty} \cap L $ of field extension $L/K$

Published on 15 Apr 2026 - 15:58

score 445 · Answer 6 · 2026-04-12 21:08:08

445

Views

Algebraic Closure is Unique up to Isomorphism in Dummit Foote

Published on 12 Apr 2026 - 21:08

score 21 · Answer 7 · 2026-04-17 01:22:28

21

Views

Prove that $[M_{j+1} : M_j] \le 2$ given $[L_{j+1} : L_j] = 2$ and $M_j = L_j \cap \mathbb{Q}(\alpha).$

Published on 17 Apr 2026 - 1:22

score 32 · Answer 8 · 2026-04-17 09:20:43

32

Views

If $\beta$ is transcendental over $F$, then is that $F(\beta)$ must be an infinite extention of $F$?

Published on 17 Apr 2026 - 9:20

score 76 · Answer 9 · 2026-04-13 17:26:02

76

Views

Is that $[\mathbb{C} : \mathbb{R}] = 2$ and is that $[\mathbb{C} : \mathbb{Q}]$ infinite?

Published on 13 Apr 2026 - 17:26

score 231 · Answer 10 · 2026-03-25 23:10:06

231

Views

A property of fields of characteristic $p$ and their extensions

Published on 25 Mar 2026 - 23:10

score 216 · Answer 11 · 2026-04-11 20:47:55

216

Views

What is the intuition behind the definiton of a seperable field extension?

Published on 11 Apr 2026 - 20:47

score 270 · Answer 12 · 2026-04-15 14:30:59

270

Views

What are the elements of $\mathbb{Q}(\sqrt[3]{2}+\sqrt{3})$?

Published on 15 Apr 2026 - 14:30

score 175 · Answer 13 · 2026-04-12 01:54:19

175

Views

Field extension of $\Bbb Q$ of degree $4$ has reals

Published on 12 Apr 2026 - 1:54

score 26 · Answer 14 · 2026-04-17 11:26:44

26

Views

How to prove $\big[\text{Frac}\left(\mathbb{F_p}[x]\right):\mathbb{F} \big]=\infty$ for a prime number $p$?

Published on 17 Apr 2026 - 11:26

score 1k · Answer 15 · 2026-04-12 01:01:53

1k

Views

Can the minimal polynomial have multiple roots?

Published on 12 Apr 2026 - 1:01

List Question

Existence of Intermediate field $F$ of $E$ and $G$ such that the $[G: F] < \infty$

Comparison of degrees of field extensions

Degree of Extension from $\mathbb{Q}$ to $\mathbb{Q}(i, \sqrt[4]2)$

Four dimensional field over complex numbers

Intermediate fields $K((K^{1/p^\infty} \cap L)^{p^\infty})$ and $K(K(L^{p^\infty}))^{1/p^\infty} \cap L $ of field extension $L/K$

Algebraic Closure is Unique up to Isomorphism in Dummit Foote

Prove that $[M_{j+1} : M_j] \le 2$ given $[L_{j+1} : L_j] = 2$ and $M_j = L_j \cap \mathbb{Q}(\alpha).$

If $\beta$ is transcendental over $F$, then is that $F(\beta)$ must be an infinite extention of $F$?

Is that $[\mathbb{C} : \mathbb{R}] = 2$ and is that $[\mathbb{C} : \mathbb{Q}]$ infinite?

A property of fields of characteristic $p$ and their extensions

What is the intuition behind the definiton of a seperable field extension?

What are the elements of $\mathbb{Q}(\sqrt[3]{2}+\sqrt{3})$?

Field extension of $\Bbb Q$ of degree $4$ has reals

How to prove $\big[\text{Frac}\left(\mathbb{F_p}[x]\right):\mathbb{F} \big]=\infty$ for a prime number $p$?

Can the minimal polynomial have multiple roots?

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