Question

$\mathbb{Q}[\sqrt{2},\sqrt{3},\dots,\sqrt{n}]=\mathbb{Q}[\sqrt{2}+\sqrt{3}+\cdots+\sqrt{n}]$

score 177 · Answer 1 · 2026-03-29 03:28:32

177

Views

$\mathbb{Q}[\sqrt{2},\sqrt{3},\dots,\sqrt{n}]=\mathbb{Q}[\sqrt{2}+\sqrt{3}+\cdots+\sqrt{n}]$

Published on 29 Mar 2026 - 3:28

score 57 · Answer 2 · 2026-03-25 14:36:43

57

Views

Can it happen that an irreducible degree $2$ polynomial becomes a perfect square in the algebraic closure?

Published on 25 Mar 2026 - 14:36

score 163 · Answer 3 · 2026-03-26 20:44:10

163

Views

If $p^k-1$ divides $p^n-1$, then $\mathbb F_{p^k}\subset \mathbb F_{p^n}$

Published on 26 Mar 2026 - 20:44

score 81 · Answer 4 · 2018-07-17 22:31:51

81

Views

Show $ax+b=0$ has only one solution

Published on 17 Jul 2018 - 22:31

score 47 · Answer 5 · 2026-03-25 02:57:23

47

Views

Integral domain $0$ element

Published on 25 Mar 2026 - 2:57

score 667 · Answer 6 · 2018-07-18 08:54:23

667

Views

Is the multiplicative identity of a subfield the multiplicative identity of the field?

Published on 18 Jul 2018 - 8:54

score 120 · Answer 7 · 2026-03-29 05:11:28

120

Views

Why is the "root field" premise necessary in this theorem about field extensions?

Published on 29 Mar 2026 - 5:11

score 407 · Answer 8 · 2018-07-18 21:03:36

407

Views

Field isomorphic to a transcendental extension of itself

Published on 18 Jul 2018 - 21:03

score 972 · Answer 9 · 2018-07-18 22:05:43

972

Views

If $K\cong K(X)$ then must $K$ be a field of rational functions in infinitely many variables?

Published on 18 Jul 2018 - 22:05

score 95 · Answer 10 · 2018-07-19 00:08:57

95

Views

What is $\mathbb{Q}(\sqrt[4]{3}i)$?

Published on 19 Jul 2018 - 0:08

score 87 · Answer 11 · 2026-03-22 23:31:58

87

Views

Creating new constants in differential field extensions via superfluous solutions to a D.E.

Published on 22 Mar 2026 - 23:31

score 36 · Answer 12 · 2026-03-28 22:28:29

36

Views

Let $K⊆M⊆L$, such that $[L:K]=n$ for some $n∈\mathbb{N}$. Prove $[M:K]$ is well-defined.

Published on 28 Mar 2026 - 22:28

score 36 · Answer 13 · 2026-03-29 03:27:11

36

Views

Property of quotient ideals in a number Field

Published on 29 Mar 2026 - 3:27

score 106 · Answer 14 · 2026-03-29 03:36:37

106

Views

Inclusion of quotient ideals. if $I \subseteq J$, then $I/qI \subseteq J/qJ$?

Published on 29 Mar 2026 - 3:36

score 58 · Answer 15 · 2026-03-25 03:22:54

58

Views

Filtered Colimit of Subalgebras

Published on 25 Mar 2026 - 3:22

List Question

$\mathbb{Q}[\sqrt{2},\sqrt{3},\dots,\sqrt{n}]=\mathbb{Q}[\sqrt{2}+\sqrt{3}+\cdots+\sqrt{n}]$

Can it happen that an irreducible degree $2$ polynomial becomes a perfect square in the algebraic closure?

If $p^k-1$ divides $p^n-1$, then $\mathbb F_{p^k}\subset \mathbb F_{p^n}$

Show $ax+b=0$ has only one solution

Integral domain $0$ element

Is the multiplicative identity of a subfield the multiplicative identity of the field?

Why is the "root field" premise necessary in this theorem about field extensions?

Field isomorphic to a transcendental extension of itself

If $K\cong K(X)$ then must $K$ be a field of rational functions in infinitely many variables?

What is $\mathbb{Q}(\sqrt[4]{3}i)$?

Creating new constants in differential field extensions via superfluous solutions to a D.E.

Let $K⊆M⊆L$, such that $[L:K]=n$ for some $n∈\mathbb{N}$. Prove $[M:K]$ is well-defined.

Property of quotient ideals in a number Field

Inclusion of quotient ideals. if $I \subseteq J$, then $I/qI \subseteq J/qJ$?

Filtered Colimit of Subalgebras

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