Question

Isomorphism classes of étale $k$-algebras with dimension $n$ such that $A\otimes_k E$ is $E$-split étale and $H^1(\text{Gal}(E/k),S_n)$

score 23 · Answer 1 · 2026-05-04 11:10:03

Isomorphism classes of étale $k$-algebras with dimension $n$ such that $A\otimes_k E$ is $E$-split étale and $H^1(\text{Gal}(E/k),S_n)$

score 125 · Answer 2 · 2026-04-14 12:01:46

125

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Is $7 + 5 \sqrt{2}$ a sum of squares in $\mathbb{Q}(\sqrt2)$?

Published on 14 Apr 2026 - 12:01

score 111 · Answer 3 · 2026-04-13 07:41:49

111

Views

How many unital $k$-subalgebras are there in $k^n$?

Published on 13 Apr 2026 - 7:41

score 142 · Answer 4 · 2026-05-11 01:53:27

142

Views

Why $[F(x):F(x^2)]=2$ if F is a field of characteristic 2?

Published on 11 May 2026 - 1:53

score 98 · Answer 5 · 2026-05-14 15:07:24

98

Views

Why the fixed elements under translation transformation $f(x) \mapsto f(x+1)$ of a field of rational functions must be constants?

Published on 14 May 2026 - 15:07

score 62 · Answer 6 · 2026-04-15 12:31:33

62

Views

Function fields of varieties and separability

Published on 15 Apr 2026 - 12:31

score 42 · Answer 7 · 2026-04-08 18:06:12

42

Views

Extending a field isomorphism

Published on 08 Apr 2026 - 18:06

score 334 · Answer 8 · 2026-04-14 23:23:21

334

Views

Finding infinitely many $\mathbb{Q}$-linearly independent polynomial preimages of the integers.

Published on 14 Apr 2026 - 23:23

score 48 · Answer 9 · 2026-04-13 11:29:18

48

Views

Open subschemes of open sets not contained in basic open sets

Published on 13 Apr 2026 - 11:29

score 142 · Answer 10 · 2026-04-17 12:33:36

142

Views

$ \sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c} = \sqrt[3]{\sqrt[3]{2} -1 } $ for rational $a,b,c$

Published on 17 Apr 2026 - 12:33

score 43 · Answer 11 · 2026-04-16 06:07:39

43

Views

Find Polynomial $P$ of a splitting field, such that deg($P$) matches $[L:K]$

Published on 16 Apr 2026 - 6:07

score 97 · Answer 12 · 2026-04-09 05:10:39

97

Views

Is $\mathbb Z[x^2]$ an ideal of $\mathbb Z[x]$?

Published on 09 Apr 2026 - 5:10

score 76 · Answer 13 · 2026-04-16 21:34:22

76

Views

Ideals of rings of continuous functions with compact support.

Published on 16 Apr 2026 - 21:34

score 117 · Answer 14 · 2026-04-15 12:35:56

117

Views

The order and the structure of $R = \mathbb F_2[x]/(x^4 + x^2 +1)$

Published on 15 Apr 2026 - 12:35

score 73 · Answer 15 · 2026-04-13 02:11:22

73

Views

The inertia degree of a field over the decomposition field

Published on 13 Apr 2026 - 2:11

List Question

Isomorphism classes of étale $k$-algebras with dimension $n$ such that $A\otimes_k E$ is $E$-split étale and $H^1(\text{Gal}(E/k),S_n)$

Is $7 + 5 \sqrt{2}$ a sum of squares in $\mathbb{Q}(\sqrt2)$?

How many unital $k$-subalgebras are there in $k^n$?

Why $[F(x):F(x^2)]=2$ if F is a field of characteristic 2?

Why the fixed elements under translation transformation $f(x) \mapsto f(x+1)$ of a field of rational functions must be constants?

Function fields of varieties and separability

Extending a field isomorphism

Finding infinitely many $\mathbb{Q}$-linearly independent polynomial preimages of the integers.

Open subschemes of open sets not contained in basic open sets

$ \sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c} = \sqrt[3]{\sqrt[3]{2} -1 } $ for rational $a,b,c$

Find Polynomial $P$ of a splitting field, such that deg($P$) matches $[L:K]$

Is $\mathbb Z[x^2]$ an ideal of $\mathbb Z[x]$?

Ideals of rings of continuous functions with compact support.

The order and the structure of $R = \mathbb F_2[x]/(x^4 + x^2 +1)$

The inertia degree of a field over the decomposition field

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