Question

Fields with respect to the operations of addition modulo $m$ and multiplication modulo $m$:

score 1.1k · Answer 1 · 2026-04-15 16:17:09

1.1k

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Fields with respect to the operations of addition modulo $m$ and multiplication modulo $m$:

Published on 15 Apr 2026 - 16:17

score 259 · Answer 2 · 2026-04-17 08:34:55

259

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Why is $\mathbb Q(\sqrt 2+\sqrt 3)=\mathbb Q(\sqrt2,\sqrt 3)$?

Published on 17 Apr 2026 - 8:34

score 253 · Answer 3 · 2026-04-16 07:33:04

253

Views

The splitting field of $p(x)=x^4+ax^2+b$ over $F$ is $F[x]/\langle p(x)\rangle$

Published on 16 Apr 2026 - 7:33

score 44 · Answer 4 · 2026-04-14 14:07:27

44

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Why $\partial_i^{[p]} = \partial_i$?

Published on 14 Apr 2026 - 14:07

score 200 · Answer 5 · 2026-04-11 11:59:34

200

Views

Representations of $F^{\times}$

Published on 11 Apr 2026 - 11:59

score 66 · Answer 6 · 2026-04-12 00:49:58

66

Views

Is $F = \{a+b\sqrt[4]{2} \mid a,b\in\mathbb{Q}\}$ a subfield of $\mathbb{R}$, the field of real numbers?

Published on 12 Apr 2026 - 0:49

score 394 · Answer 7 · 2026-04-14 01:42:41

394

Views

GF(2) is a field, binary field

Published on 14 Apr 2026 - 1:42

score 461 · Answer 8 · 2026-04-16 08:11:20

461

Views

Not really sure what a $k[x]$-module is.

Published on 16 Apr 2026 - 8:11

score 51 · Answer 9 · 2026-04-16 21:08:58

51

Views

Factor $X^5+6X^3+15X^2+3$ in $\mathbb{Q}\left (\sqrt{-3},\sqrt{-2}\right )\left [X\right ]$?

Published on 16 Apr 2026 - 21:08

score 31 · Answer 10 · 2026-04-12 06:10:48

31

Views

$\left [\mathbb{Z}\left [i\right ]/\left (a\right ):K\right ]$, $a$ irreducible, $K$ prime field

Published on 12 Apr 2026 - 6:10

score 79 · Answer 11 · 2026-04-22 19:41:02

79

Views

Why is : $ [ \mathbb{R} [x_1 , \dots , x_n ]^{ A_n } : \mathbb{R} [x_1 , \dots , x_n ]^{ S_n } ] = [ \mathfrak{S}_n : \mathfrak{A}_n ] $?

Published on 22 Apr 2026 - 19:41

score 170 · Answer 12 · 2026-03-26 17:53:56

170

Views

If $x$ is transcendental and $y$ is algebraic, what about $x+y$ and $xy$?

Published on 26 Mar 2026 - 17:53

score 110 · Answer 13 · 2026-03-26 17:53:53

110

Views

If $x$ and $y$ are transcendental, then $\left \{x,y\right \}$ is algebraically independent?

Published on 26 Mar 2026 - 17:53

score 517 · Answer 14 · 2026-04-16 09:10:32

517

Views

Using the tower law with field extensions

Published on 16 Apr 2026 - 9:10

score 593 · Answer 15 · 2026-04-16 06:28:07

593

Views

Counting The Number of Non-invertible matrices

Published on 16 Apr 2026 - 6:28

List Question

Fields with respect to the operations of addition modulo $m$ and multiplication modulo $m$:

Why is $\mathbb Q(\sqrt 2+\sqrt 3)=\mathbb Q(\sqrt2,\sqrt 3)$?

The splitting field of $p(x)=x^4+ax^2+b$ over $F$ is $F[x]/\langle p(x)\rangle$

Why $\partial_i^{[p]} = \partial_i$?

Representations of $F^{\times}$

Is $F = \{a+b\sqrt[4]{2} \mid a,b\in\mathbb{Q}\}$ a subfield of $\mathbb{R}$, the field of real numbers?

GF(2) is a field, binary field

Not really sure what a $k[x]$-module is.

Factor $X^5+6X^3+15X^2+3$ in $\mathbb{Q}\left (\sqrt{-3},\sqrt{-2}\right )\left [X\right ]$?

$\left [\mathbb{Z}\left [i\right ]/\left (a\right ):K\right ]$, $a$ irreducible, $K$ prime field

Why is : $ [ \mathbb{R} [x_1 , \dots , x_n ]^{ A_n } : \mathbb{R} [x_1 , \dots , x_n ]^{ S_n } ] = [ \mathfrak{S}_n : \mathfrak{A}_n ] $?

If $x$ is transcendental and $y$ is algebraic, what about $x+y$ and $xy$?

If $x$ and $y$ are transcendental, then $\left \{x,y\right \}$ is algebraically independent?

Using the tower law with field extensions

Counting The Number of Non-invertible matrices

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