Question

How to show that $\sqrt{2}$ is not in $\mathbb Q(\sqrt{3},\sqrt{5})$?

score 791 · Answer 1 · 2026-03-31 11:01:38

791

Views

How to show that $\sqrt{2}$ is not in $\mathbb Q(\sqrt{3},\sqrt{5})$?

Published on 31 Mar 2026 - 11:01

score 109 · Answer 2 · 2019-03-31 14:29:46

109

Views

Two questions about a proof that "if a polynomial is the zero function, all of its components are zero."

Published on 31 Mar 2019 - 14:29

score 130 · Answer 3 · 2019-03-31 23:36:39

If $F$ is a field, $E$ an extension field of $F$, and $u \in E$ transcendental over $F$, then $F(u) = \{f(u)g(u)^{-1}|f,g \in F[x]; g \neq 0\}$

score 123 · Answer 4 · 2026-03-31 19:15:08

123

Views

$\mathbb{F}_{3}[x]/(x^3-x^2+1) \cong \mathbb{F}_{3}[x]/(x^3-x^2+x+1)$.

Published on 31 Mar 2026 - 19:15

score 977 · Answer 5 · 2026-03-28 14:19:39

977

Views

Show that $x^{p^m} - x$ divides $x^{p^n} - x$ if and only if $m$ divides $n$.

Published on 28 Mar 2026 - 14:19

score 81 · Answer 6 · 2026-03-28 14:18:24

81

Views

Precisely which polynomials vanish on $\mathbb{F}_{p^n}$?

Published on 28 Mar 2026 - 14:18

score 39 · Answer 7 · 2026-03-31 11:04:39

39

Views

Let $k \subseteq F \subseteq K$ be fields, and let $z \in K$. Prove that if $k(z) \colon k$ is finite, then $[F(z):F] \leq [k(z):k]$.

Published on 31 Mar 2026 - 11:04

score 1.8k · Answer 8 · 2026-03-25 20:35:34

1.8k

Views

Impossibility of constructing certain regular polygons with straight-edge and compass

Published on 25 Mar 2026 - 20:35

score 21 · Answer 9 · 2026-03-25 04:43:32

21

Views

Definition of universe of field of fractions (lost in translation)

Published on 25 Mar 2026 - 4:43

score 316 · Answer 10 · 2019-04-02 12:19:49

316

Views

Field Extensions with $\sqrt{2}$

Published on 02 Apr 2019 - 12:19

score 460 · Answer 11 · 2019-04-02 20:57:20

460

Views

Injective field homomorphism implies surjective?

Published on 02 Apr 2019 - 20:57

score 146 · Answer 12 · 2026-03-31 21:05:16

146

Views

Problem 15 from Lang's Algebra

Published on 31 Mar 2026 - 21:05

score 221 · Answer 13 · 2026-03-26 21:35:04

221

Views

Algebraic closure of $\mathbb{Q}$ in $\mathbb{Q}_p$

Published on 26 Mar 2026 - 21:35

score 80 · Answer 14 · 2019-04-03 10:54:48

80

Views

How does the product $q_j X^j_m$ make sense in this context?

Published on 03 Apr 2019 - 10:54

score 236 · Answer 15 · 2026-03-25 19:04:17

236

Views

Invariant subspace in $K\otimes V$ is generated by invariant vectors?

Published on 25 Mar 2026 - 19:04

List Question

How to show that $\sqrt{2}$ is not in $\mathbb Q(\sqrt{3},\sqrt{5})$?

Two questions about a proof that "if a polynomial is the zero function, all of its components are zero."

If $F$ is a field, $E$ an extension field of $F$, and $u \in E$ transcendental over $F$, then $F(u) = \{f(u)g(u)^{-1}|f,g \in F[x]; g \neq 0\}$

$\mathbb{F}_{3}[x]/(x^3-x^2+1) \cong \mathbb{F}_{3}[x]/(x^3-x^2+x+1)$.

Show that $x^{p^m} - x$ divides $x^{p^n} - x$ if and only if $m$ divides $n$.

Precisely which polynomials vanish on $\mathbb{F}_{p^n}$?

Let $k \subseteq F \subseteq K$ be fields, and let $z \in K$. Prove that if $k(z) \colon k$ is finite, then $[F(z):F] \leq [k(z):k]$.

Impossibility of constructing certain regular polygons with straight-edge and compass

Definition of universe of field of fractions (lost in translation)

Field Extensions with $\sqrt{2}$

Injective field homomorphism implies surjective?

Problem 15 from Lang's Algebra

Algebraic closure of $\mathbb{Q}$ in $\mathbb{Q}_p$

How does the product $q_j X^j_m$ make sense in this context?

Invariant subspace in $K\otimes V$ is generated by invariant vectors?

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