Question

Is $F$ over $\mathbb{F}_2(x)$ separable?

score 93 · Answer 1 · 2026-04-13 18:18:02

93

Views

Is $F$ over $\mathbb{F}_2(x)$ separable?

Published on 13 Apr 2026 - 18:18

score 46 · Answer 2 · 2026-04-15 22:08:24

46

Views

How many different roots does $p(x) = x^{12}+2x^{6}+1 \in \mathbb{F}_3[x]$ have?

Published on 15 Apr 2026 - 22:08

score 100 · Answer 3 · 2026-04-17 09:45:55

100

Views

Discriminant of the minimal polynomial in simple extension

Published on 17 Apr 2026 - 9:45

score 155 · Answer 4 · 2026-04-15 00:51:09

155

Views

Construct the splitting field for the polynomial of $x^4-3$ over $\mathbb{Q}$?

Published on 15 Apr 2026 - 0:51

score 30 · Answer 5 · 2026-04-15 17:22:09

30

Views

For polynomials $f(x), p(x)$ in a polynomial ring $K[X]$, $K$ a field, where $p(x)|f(x)$ does it then imply that $\frac{f(x)}{p(x)} \in K[X]$ aswel?

Published on 15 Apr 2026 - 17:22

score 102 · Answer 6 · 2026-04-16 05:25:54

102

Views

Fields and Irreducible Polynomials

Published on 16 Apr 2026 - 5:25

score 196 · Answer 7 · 2026-04-15 16:04:52

196

Views

Constructing Finite Separable Field Extensions From Sets Equipped With a Continuous Galois Group Action

Published on 15 Apr 2026 - 16:04

score 25 · Answer 8 · 2026-04-14 16:03:25

25

Views

($a$ - algebraic element and $I_a$ - maximal ideal) => ($K[a]$ is isomorphic with $K[x]/I_a$)

Published on 14 Apr 2026 - 16:03

score 79 · Answer 9 · 2026-04-16 04:29:23

If $\mathbb{K}$ is an extension of $\mathbb{Q}$ of degree $15$, which of these elements cannot belong to $\mathbb{K}$?

score 33 · Answer 10 · 2026-04-11 16:52:25

33

Views

Dimensions and Basis of fields short questions

Published on 11 Apr 2026 - 16:52

score 151 · Answer 11 · 2026-04-11 19:00:29

151

Views

Simple extension of purely inseparable extension

Published on 11 Apr 2026 - 19:00

score 92 · Answer 12 · 2026-04-14 13:47:12

92

Views

Finding an example of a cyclic extension over $\mathbb{Q}_p$ of prime power degree which is neither unramified nor totally ramified

Published on 14 Apr 2026 - 13:47

score 40 · Answer 13 · 2026-04-16 01:09:28

40

Views

Subgroups of Gal($\mathbb{Q}(\xi_{12})/\mathbb{Q})$

Published on 16 Apr 2026 - 1:09

score 41 · Answer 14 · 2026-04-12 06:58:25

41

Views

Field extension using irreducible polynomials

Published on 12 Apr 2026 - 6:58

score 73 · Answer 15 · 2026-04-16 22:31:40

73

Views

$\mathbb{Q}$-automorphisms on $\mathbb{Q}(x_1, ..., x_n)$ map one-to-one into $S_n$

Published on 16 Apr 2026 - 22:31

List Question

Is $F$ over $\mathbb{F}_2(x)$ separable?

How many different roots does $p(x) = x^{12}+2x^{6}+1 \in \mathbb{F}_3[x]$ have?

Discriminant of the minimal polynomial in simple extension

Construct the splitting field for the polynomial of $x^4-3$ over $\mathbb{Q}$?

For polynomials $f(x), p(x)$ in a polynomial ring $K[X]$, $K$ a field, where $p(x)|f(x)$ does it then imply that $\frac{f(x)}{p(x)} \in K[X]$ aswel?

Fields and Irreducible Polynomials

Constructing Finite Separable Field Extensions From Sets Equipped With a Continuous Galois Group Action

($a$ - algebraic element and $I_a$ - maximal ideal) => ($K[a]$ is isomorphic with $K[x]/I_a$)

If $\mathbb{K}$ is an extension of $\mathbb{Q}$ of degree $15$, which of these elements cannot belong to $\mathbb{K}$?

Dimensions and Basis of fields short questions

Simple extension of purely inseparable extension

Finding an example of a cyclic extension over $\mathbb{Q}_p$ of prime power degree which is neither unramified nor totally ramified

Subgroups of Gal($\mathbb{Q}(\xi_{12})/\mathbb{Q})$

Field extension using irreducible polynomials

$\mathbb{Q}$-automorphisms on $\mathbb{Q}(x_1, ..., x_n)$ map one-to-one into $S_n$

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