Question

Field is perfect iff every element has pth root.

score 312 · Answer 1 · 2026-02-23 02:54:22

312

Views

Field is perfect iff every element has pth root.

Published on 23 Feb 2026 - 2:54

score 55 · Answer 2 · 2019-03-19 03:49:01

55

Views

Is $\mathbb{Q}(i,\sqrt[3]{2})=\mathbb{Q}(i,\sqrt[3]{4})$?

Published on 19 Mar 2019 - 3:49

score 62 · Answer 3 · 2019-03-19 15:38:15

62

Views

What is the use of extension of the real and complex field?

Published on 19 Mar 2019 - 15:38

score 111 · Answer 4 · 2026-04-02 10:38:07

111

Views

$K=\Bbb Q(\sqrt3,\sqrt[3]{2}) $, Compute $[K:\Bbb Q]$.

Published on 02 Apr 2026 - 10:38

score 258 · Answer 5 · 2026-03-27 17:04:59

258

Views

Normal Closure of an Algebraic Extension

Published on 27 Mar 2026 - 17:04

score 44 · Answer 6 · 2019-03-20 15:07:48

44

Views

$[\mathbb{F}_{p}(\alpha,\beta)$:$ \mathbb{F}_{p}]=\text{lcm}(m,n) $ and $[\mathbb{F}_{p}(\alpha)∩\mathbb{F}_{p}(\beta)$:$ \mathbb{F}_{p}]=\gcd(m,n)$

Published on 20 Mar 2019 - 15:07

score 105 · Answer 7 · 2019-03-20 20:57:29

105

Views

Is it true that a finite field extension with degree $>1$ cannot be isomorphic to its base field?

Published on 20 Mar 2019 - 20:57

score 168 · Answer 8 · 2019-03-21 00:54:10

168

Views

A field with 729 elements

Published on 21 Mar 2019 - 0:54

score 51 · Answer 9 · 2019-03-21 06:02:25

51

Views

Prove that $S = \{A \in GL_n(K) | AJA^t = J\}$ is a subgroup of $GL_n(K)$

Published on 21 Mar 2019 - 6:02

score 261 · Answer 10 · 2019-03-21 08:26:47

261

Views

Does an uncountable algebraically closed field of characteristic zero contain an uncountable subfield which can be embedded into $\mathbb{C}$?

Published on 21 Mar 2019 - 8:26

score 1.2k · Answer 11 · 2019-03-21 10:20:43

1.2k

Views

What fields between the rationals and the reals allow to define the usual 2D distance?

Published on 21 Mar 2019 - 10:20

score 676 · Answer 12 · 2019-03-21 12:44:15

676

Views

Is there a cubic irreducible polynomial over $\Bbb Q$ with all of its three roots are irrational?

Published on 21 Mar 2019 - 12:44

score 232 · Answer 13 · 2026-03-31 08:51:56

232

Views

Degree of $\mathbb{Q}(\sqrt{2 + \sqrt{7}})$ and splitting field

Published on 31 Mar 2026 - 8:51

score 403 · Answer 14 · 2026-03-25 12:24:01

403

Views

Kernel of a polynomial ring homomorphism

Published on 25 Mar 2026 - 12:24

score 101 · Answer 15 · 2026-04-01 23:13:16

101

Views

If $f(x) \in\Bbb Q[x]$ has splitting field of degree $16$ over $\Bbb Q$ is $f(x)$ solvable by radicals?

Published on 01 Apr 2026 - 23:13

List Question

Field is perfect iff every element has pth root.

Is $\mathbb{Q}(i,\sqrt[3]{2})=\mathbb{Q}(i,\sqrt[3]{4})$?

What is the use of extension of the real and complex field?

$K=\Bbb Q(\sqrt3,\sqrt[3]{2}) $, Compute $[K:\Bbb Q]$.

Normal Closure of an Algebraic Extension

$[\mathbb{F}_{p}(\alpha,\beta)$:$ \mathbb{F}_{p}]=\text{lcm}(m,n) $ and $[\mathbb{F}_{p}(\alpha)∩\mathbb{F}_{p}(\beta)$:$ \mathbb{F}_{p}]=\gcd(m,n)$

Is it true that a finite field extension with degree $>1$ cannot be isomorphic to its base field?

A field with 729 elements

Prove that $S = \{A \in GL_n(K) | AJA^t = J\}$ is a subgroup of $GL_n(K)$

Does an uncountable algebraically closed field of characteristic zero contain an uncountable subfield which can be embedded into $\mathbb{C}$?

What fields between the rationals and the reals allow to define the usual 2D distance?

Is there a cubic irreducible polynomial over $\Bbb Q$ with all of its three roots are irrational?

Degree of $\mathbb{Q}(\sqrt{2 + \sqrt{7}})$ and splitting field

Kernel of a polynomial ring homomorphism

If $f(x) \in\Bbb Q[x]$ has splitting field of degree $16$ over $\Bbb Q$ is $f(x)$ solvable by radicals?

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