Question

Characteristic of a field is either $0$ or prime $p$.

score 669 · Answer 1 · 2019-04-17 03:52:51

669

Views

Characteristic of a field is either $0$ or prime $p$.

Published on 17 Apr 2019 - 3:52

score 731 · Answer 2 · 2026-03-28 01:02:53

731

Views

Show that $E/F$ is Galois extension

Published on 28 Mar 2026 - 1:02

score 1.2k · Answer 3 · 2026-03-27 00:02:57

1.2k

Views

Is $x^3-1$ reducible over $\mathbb{Q}$

Published on 27 Mar 2026 - 0:02

score 78 · Answer 4 · 2026-03-25 22:25:10

78

Views

Clarification on normality and separability in the context of field extensions.

Published on 25 Mar 2026 - 22:25

score 61 · Answer 5 · 2026-03-31 15:18:36

61

Views

Let $F = \mathbb{Q}(a_1, a_2, . . . , a_n)$ with $a_i^2 \in \mathbb{Q}.$ Prove that $ \sqrt[3]2 \notin F$.

Published on 31 Mar 2026 - 15:18

score 14 · Answer 6 · 2026-03-03 12:21:27

14

Views

Let $E = \{a_0+a_1t+a_2t^2|a_i \in \Bbb Z_2 | t^3=1+t \}$, find the roots of $g(x)=x^2+tx+1+t^2$.

Published on 03 Mar 2026 - 12:21

score 3.5k · Answer 7 · 2019-04-18 17:51:53

3.5k

Views

Show that $\mathbb{Q}[\sqrt{2}] = \{a + b\sqrt{2}\}$ is a vector space over $\mathbb{Q}.$

Published on 18 Apr 2019 - 17:51

score 455 · Answer 8 · 2026-03-28 01:02:52

455

Views

A question regarding the Galois extension of the cyclotomic polynomial $\Phi_{15}$

Published on 28 Mar 2026 - 1:02

score 167 · Answer 9 · 2026-03-28 17:42:00

167

Views

Factorization of a polynomial in $\Bbb F_7$

Published on 28 Mar 2026 - 17:42

score 344 · Answer 10 · 2019-04-18 20:04:17

344

Views

How to show the fixed field is a subfield

Published on 18 Apr 2019 - 20:04

score 24 · Answer 11 · 2019-04-18 21:27:13

24

Views

Determine all idempotents, nilpotents, and units in $F[x]/\langle h\rangle$, where $F$ is a field, $h=x^2-x$.

Published on 18 Apr 2019 - 21:27

score 26 · Answer 12 · 2019-04-18 21:45:29

26

Views

Finding an element in an extension of the rationals

Published on 18 Apr 2019 - 21:45

score 242 · Answer 13 · 2026-03-25 06:04:41

242

Views

What is the Galois group of the Hyperreal Numbers?

Published on 25 Mar 2026 - 6:04

score 64 · Answer 14 · 2026-03-25 23:58:39

64

Views

For a field $K$ of characteristics $p>0$, when is a finite purely inseparable extension $F/K$ (with $[F:K]=p^n>1$) such that $F\cong K$?

Published on 25 Mar 2026 - 23:58

score 43 · Answer 15 · 2019-04-19 17:05:14

43

Views

Sums of norms of zeros of polynomial

Published on 19 Apr 2019 - 17:05

List Question

Characteristic of a field is either $0$ or prime $p$.

Show that $E/F$ is Galois extension

Is $x^3-1$ reducible over $\mathbb{Q}$

Clarification on normality and separability in the context of field extensions.

Let $F = \mathbb{Q}(a_1, a_2, . . . , a_n)$ with $a_i^2 \in \mathbb{Q}.$ Prove that $ \sqrt[3]2 \notin F$.

Let $E = \{a_0+a_1t+a_2t^2|a_i \in \Bbb Z_2 | t^3=1+t \}$, find the roots of $g(x)=x^2+tx+1+t^2$.

Show that $\mathbb{Q}[\sqrt{2}] = \{a + b\sqrt{2}\}$ is a vector space over $\mathbb{Q}.$

A question regarding the Galois extension of the cyclotomic polynomial $\Phi_{15}$

Factorization of a polynomial in $\Bbb F_7$

How to show the fixed field is a subfield

Determine all idempotents, nilpotents, and units in $F[x]/\langle h\rangle$, where $F$ is a field, $h=x^2-x$.

Finding an element in an extension of the rationals

What is the Galois group of the Hyperreal Numbers?

For a field $K$ of characteristics $p>0$, when is a finite purely inseparable extension $F/K$ (with $[F:K]=p^n>1$) such that $F\cong K$?

Sums of norms of zeros of polynomial

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