Question

Prove that $\mathbb Q[x]/\langle x^3+x^2-2x-1\rangle$ cannot be obtained by adjoining any cube root of rational number

score 239 · Answer 1 · 2026-04-16 20:51:42

239

Views

Prove that $\mathbb Q[x]/\langle x^3+x^2-2x-1\rangle$ cannot be obtained by adjoining any cube root of rational number

Published on 16 Apr 2026 - 20:51

score 1k · Answer 2 · 2026-04-12 23:38:19

1k

Views

(Proof Verification) Prove that the sum of two algebraic numbers is algebraic.

Published on 12 Apr 2026 - 23:38

score 69 · Answer 3 · 2026-04-16 00:54:18

69

Views

Which of the following is a degree-100 extension of $\Bbb Q(i)$?

Published on 16 Apr 2026 - 0:54

score 118 · Answer 4 · 2026-04-16 18:19:49

118

Views

How many roots does $f=x^4+x^2+2$ have in $\mathbb Q[x]/(f)$?

Published on 16 Apr 2026 - 18:19

score 158 · Answer 5 · 2026-04-13 11:07:34

158

Views

Roots for polynomial of coefficients in non integral domain

Published on 13 Apr 2026 - 11:07

score 209 · Answer 6 · 2026-04-14 14:27:56

209

Views

The cardinality of an algebraic extension $E$ of a field $F$ cannot exceed the cardinality of $F[X]$

Published on 14 Apr 2026 - 14:27

score 601 · Answer 7 · 2026-04-11 23:44:46

601

Views

The left adjoint of the restriction functor in field extension

Published on 11 Apr 2026 - 23:44

score 298 · Answer 8 · 2026-04-16 23:28:56

298

Views

Find an example of degree-100 extension of $\Bbb Q(\zeta_5)$ and $\Bbb Q(\sqrt[3]{2})$.

Published on 16 Apr 2026 - 23:28

score 120 · Answer 9 · 2026-04-15 20:55:48

120

Views

Embedding of $K(\alpha)\hookrightarrow \bar{K}$ fixing $K$

Published on 15 Apr 2026 - 20:55

score 308 · Answer 10 · 2026-04-11 21:47:35

308

Views

Separable Algebra

Published on 11 Apr 2026 - 21:47

score 200 · Answer 11 · 2026-04-09 12:27:00

200

Views

Separable Algebra, Equivalence of Definitions

Published on 09 Apr 2026 - 12:27

score 143 · Answer 12 · 2026-04-11 02:02:38

143

Views

What is the relationship between the minimal polynomial of $\alpha$ and the minimal polynomial of a linear function of $\alpha$?

Published on 11 Apr 2026 - 2:02

score 36 · Answer 13 · 2026-03-25 19:51:39

36

Views

$(k^s)^p$ generates $k^s$ over $k$ if $k$ is $F$-finite?

Published on 25 Mar 2026 - 19:51

score 220 · Answer 14 · 2026-04-14 20:49:52

220

Views

How to show that $\mathbb{Z}\left[\frac{1 + \sqrt{5}}{2}\right]$ is finitely generated?

Published on 14 Apr 2026 - 20:49

score 142 · Answer 15 · 2026-04-14 07:37:03

142

Views

Embedding problem for two algebraically closed fields

Published on 14 Apr 2026 - 7:37

List Question

Prove that $\mathbb Q[x]/\langle x^3+x^2-2x-1\rangle$ cannot be obtained by adjoining any cube root of rational number

(Proof Verification) Prove that the sum of two algebraic numbers is algebraic.

Which of the following is a degree-100 extension of $\Bbb Q(i)$?

How many roots does $f=x^4+x^2+2$ have in $\mathbb Q[x]/(f)$?

Roots for polynomial of coefficients in non integral domain

The cardinality of an algebraic extension $E$ of a field $F$ cannot exceed the cardinality of $F[X]$

The left adjoint of the restriction functor in field extension

Find an example of degree-100 extension of $\Bbb Q(\zeta_5)$ and $\Bbb Q(\sqrt[3]{2})$.

Embedding of $K(\alpha)\hookrightarrow \bar{K}$ fixing $K$

Separable Algebra

Separable Algebra, Equivalence of Definitions

What is the relationship between the minimal polynomial of $\alpha$ and the minimal polynomial of a linear function of $\alpha$?

$(k^s)^p$ generates $k^s$ over $k$ if $k$ is $F$-finite?

How to show that $\mathbb{Z}\left[\frac{1 + \sqrt{5}}{2}\right]$ is finitely generated?

Embedding problem for two algebraically closed fields

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