Question

Confusion over field isomorphism F(a) onto F(b) where a and b are roots of an irreducible polynomial in F[t]?

score 363 · Answer 1 · 2026-04-16 14:47:08

363

Views

Confusion over field isomorphism F(a) onto F(b) where a and b are roots of an irreducible polynomial in F[t]?

Published on 16 Apr 2026 - 14:47

score 264 · Answer 2 · 2026-04-15 12:08:19

264

Views

Why is it that if $\alpha$ is a root with minimal polynomial of degree $2^k$ (for some integer $k$), then $\alpha$ is constructible?

Published on 15 Apr 2026 - 12:08

score 966 · Answer 3 · 2026-04-14 22:14:35

966

Views

What fields are isomorphic to $\mathbb{Q}[\sqrt{2}]$ other than $\mathbb{Q}[\sqrt{2}]$ itself?

Published on 14 Apr 2026 - 22:14

score 189 · Answer 4 · 2026-03-29 16:00:52

189

Views

Existence of intermediate fields with order $9$ and $3$ of a Galois field extension of order $27$.

Published on 29 Mar 2026 - 16:00

score 166 · Answer 5 · 2026-04-15 20:35:20

166

Views

Galois extension $\frac{\mathbb Z_2[x]}{\langle 1+x+x^3 \rangle}:\mathbb Z_2$

Published on 15 Apr 2026 - 20:35

score 805 · Answer 6 · 2026-04-14 08:11:33

805

Views

Completion of field equals completion of extension

Published on 14 Apr 2026 - 8:11

score 107 · Answer 7 · 2026-03-25 12:52:09

107

Views

Is $\mathbb Z_7$ an extension of $\mathbb Z_2$?

Published on 25 Mar 2026 - 12:52

score 79 · Answer 8 · 2026-04-13 18:24:13

79

Views

Can you construct linear operators from arbitrary modules over rings?

Published on 13 Apr 2026 - 18:24

score 2k · Answer 9 · 2026-04-14 02:43:36

2k

Views

Galois, normal and separable extensions

Published on 14 Apr 2026 - 2:43

score 46 · Answer 10 · 2026-04-16 03:06:44

$\mathbb{R}(A/B)$ $=$ $\mathbb{R}\left(\frac{\alpha A+\beta B}{\gamma A + \delta B}\right)$, if $ \alpha \delta − \beta \gamma \neq 0$

score 771 · Answer 11 · 2026-04-12 18:08:04

771

Views

Galois Theory: Prove that every finite extension over $F$ is cyclic (more details in question)

Published on 12 Apr 2026 - 18:08

score 273 · Answer 12 · 2026-04-16 18:12:13

273

Views

The possible degrees of $\mathbb{Q}(a,b)$ in terms of the degrees of $a$ and $b$

Published on 16 Apr 2026 - 18:12

score 217 · Answer 13 · 2026-04-15 14:07:48

217

Views

constructing the Galois group for $\mathbb{Q}(\sqrt2, \sqrt[3]2)$

Published on 15 Apr 2026 - 14:07

score 68 · Answer 14 · 2026-04-10 01:04:01

68

Views

About the logic structure of a Theorem

Published on 10 Apr 2026 - 1:04

score 157 · Answer 15 · 2026-04-14 09:20:42

157

Views

Analog of Kronecker's Theorem for Polynomials over an Algebra

Published on 14 Apr 2026 - 9:20

List Question

Confusion over field isomorphism F(a) onto F(b) where a and b are roots of an irreducible polynomial in F[t]?

Why is it that if $\alpha$ is a root with minimal polynomial of degree $2^k$ (for some integer $k$), then $\alpha$ is constructible?

What fields are isomorphic to $\mathbb{Q}[\sqrt{2}]$ other than $\mathbb{Q}[\sqrt{2}]$ itself?

Existence of intermediate fields with order $9$ and $3$ of a Galois field extension of order $27$.

Galois extension $\frac{\mathbb Z_2[x]}{\langle 1+x+x^3 \rangle}:\mathbb Z_2$

Completion of field equals completion of extension

Is $\mathbb Z_7$ an extension of $\mathbb Z_2$?

Can you construct linear operators from arbitrary modules over rings?

Galois, normal and separable extensions

$\mathbb{R}(A/B)$ $=$ $\mathbb{R}\left(\frac{\alpha A+\beta B}{\gamma A + \delta B}\right)$, if $ \alpha \delta − \beta \gamma \neq 0$

Galois Theory: Prove that every finite extension over $F$ is cyclic (more details in question)

The possible degrees of $\mathbb{Q}(a,b)$ in terms of the degrees of $a$ and $b$

constructing the Galois group for $\mathbb{Q}(\sqrt2, \sqrt[3]2)$

About the logic structure of a Theorem

Analog of Kronecker's Theorem for Polynomials over an Algebra

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