Question

Given $f \in \mathbb{Q}[x]$ irreducible. How many and which roots of $f$ are contained in $\mathbb{Q}[x]/(f)$?

score 91 · Answer 1 · 2026-04-17 11:13:46

91

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Given $f \in \mathbb{Q}[x]$ irreducible. How many and which roots of $f$ are contained in $\mathbb{Q}[x]/(f)$?

Published on 17 Apr 2026 - 11:13

score 2.8k · Answer 2 · 2026-04-16 12:13:11

2.8k

Views

Transcendental extension, rational functions and field tower

Published on 16 Apr 2026 - 12:13

score 153 · Answer 3 · 2026-04-13 01:50:27

153

Views

Splitting field, polynomials

Published on 13 Apr 2026 - 1:50

score 294 · Answer 4 · 2026-04-14 09:44:18

294

Views

What power can have irreducible polynomials over a subfield of an algebraically closed field?

Published on 14 Apr 2026 - 9:44

score 1.4k · Answer 5 · 2026-04-13 20:02:02

1.4k

Views

Example of composition of two normal field extensions which is not normal.

Published on 13 Apr 2026 - 20:02

score 629 · Answer 6 · 2026-04-14 00:42:02

629

Views

Question about the proof that $K(u)$ is isomorphic to $K(x)$ if u is transcendental over $K$.

Published on 14 Apr 2026 - 0:42

score 105 · Answer 7 · 2026-04-09 21:53:02

105

Views

Composition of Number Fields

Published on 09 Apr 2026 - 21:53

score 484 · Answer 8 · 2026-04-12 18:39:51

484

Views

Algebraic and Galois Extension is a Splitting Field of some set.

Published on 12 Apr 2026 - 18:39

score 171 · Answer 9 · 2026-04-17 11:44:15

171

Views

$[\mathbb{Q}(\alpha, \beta):\mathbb{Q}(\alpha)]\mid [\mathbb{Q}(\beta):\mathbb{Q}]$?

Published on 17 Apr 2026 - 11:44

score 305 · Answer 10 · 2026-04-18 20:05:38

305

Views

Finding the order of an irreducible polynomial $f$ in $F_3[x]$ of degree 4?

Published on 18 Apr 2026 - 20:05

score 231 · Answer 11 · 2026-04-18 20:05:38

231

Views

Proving $f = x^8+x^7+x^3+x+1$ to be irreducible over $\mathbf{F}_2$.

Published on 18 Apr 2026 - 20:05

score 2.3k · Answer 12 · 2026-04-08 20:48:32

2.3k

Views

composition of field extensions

Published on 08 Apr 2026 - 20:48

score 274 · Answer 13 · 2026-04-15 00:00:31

274

Views

algebraic element over a field

Published on 15 Apr 2026 - 0:00

score 1.4k · Answer 14 · 2026-04-17 07:57:25

1.4k

Views

Smallest subfield containing $F$ and $\alpha$

Published on 17 Apr 2026 - 7:57

score 1k · Answer 15 · 2026-04-14 15:34:58

1k

Views

Classification of fields which are isomorphic to some finite extension

Published on 14 Apr 2026 - 15:34

List Question

Given $f \in \mathbb{Q}[x]$ irreducible. How many and which roots of $f$ are contained in $\mathbb{Q}[x]/(f)$?

Transcendental extension, rational functions and field tower

Splitting field, polynomials

What power can have irreducible polynomials over a subfield of an algebraically closed field?

Example of composition of two normal field extensions which is not normal.

Question about the proof that $K(u)$ is isomorphic to $K(x)$ if u is transcendental over $K$.

Composition of Number Fields

Algebraic and Galois Extension is a Splitting Field of some set.

$[\mathbb{Q}(\alpha, \beta):\mathbb{Q}(\alpha)]\mid [\mathbb{Q}(\beta):\mathbb{Q}]$?

Finding the order of an irreducible polynomial $f$ in $F_3[x]$ of degree 4?

Proving $f = x^8+x^7+x^3+x+1$ to be irreducible over $\mathbf{F}_2$.

composition of field extensions

algebraic element over a field

Smallest subfield containing $F$ and $\alpha$

Classification of fields which are isomorphic to some finite extension

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