Question

Proof that $F(a)\approx F[x]/\langle p(x) \rangle$

score 1.1k · Answer 1 · 2026-04-15 16:19:17

1.1k

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Proof that $F(a)\approx F[x]/\langle p(x) \rangle$

Published on 15 Apr 2026 - 16:19

score 558 · Answer 2 · 2026-04-13 16:36:57

558

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order of automorphism group and index of finite field extension

Published on 13 Apr 2026 - 16:36

score 3.9k · Answer 3 · 2026-04-15 03:55:54

3.9k

Views

show that if $K$ is a field then $K[x]$ is principal

Published on 15 Apr 2026 - 3:55

score 120 · Answer 4 · 2026-04-15 09:04:46

120

Views

Must an irreducible polynomial over a field extension divide the irreducible polynomial over the subfield?

Published on 15 Apr 2026 - 9:04

score 683 · Answer 5 · 2026-05-11 07:21:32

683

Views

Can a field with cardinality $3$ be an ordered field?

Published on 11 May 2026 - 7:21

score 65 · Answer 6 · 2026-04-14 03:56:29

65

Views

Is $\mathbb{F}$ an algebraic extension of $k$ if $\dim_k V < |k|$?

Published on 14 Apr 2026 - 3:56

score 420 · Answer 7 · 2026-04-23 04:57:30

420

Views

What is a Module, and what is an R-module? (understanding the definition)

Published on 23 Apr 2026 - 4:57

score 1.1k · Answer 8 · 2026-04-08 23:38:44

1.1k

Views

$\mathbb{Z}[\zeta]$ is not a UFD

Published on 08 Apr 2026 - 23:38

score 84 · Answer 9 · 2026-04-23 04:56:12

84

Views

Question about the definition of free modules

Published on 23 Apr 2026 - 4:56

score 1.1k · Answer 10 · 2026-04-15 16:22:58

1.1k

Views

If there exists a cyclic extension of degree $p$ of $K$, then there exists a cyclic extension of degree $p^n$ for every $n\ge 1$?

Published on 15 Apr 2026 - 16:22

score 116 · Answer 11 · 2026-04-15 06:04:07

116

Views

field extension Q(∛2) of Q

Published on 15 Apr 2026 - 6:04

score 247 · Answer 12 · 2026-04-15 19:39:27

247

Views

Example of a nontransitive action of $\operatorname{Aut}(K/\mathbb Q)$ on the roots in $K$ of an irreducible polynomial.

Published on 15 Apr 2026 - 19:39

score 46 · Answer 13 · 2026-04-10 20:02:04

46

Views

A query about generalizing the complex field

Published on 10 Apr 2026 - 20:02

score 121 · Answer 14 · 2026-04-12 03:22:12

121

Views

Field Theory: Common root (element of field extension) of two polynomials

Published on 12 Apr 2026 - 3:22

score 2.4k · Answer 15 · 2026-04-17 22:29:05

2.4k

Views

Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension

Published on 17 Apr 2026 - 22:29

List Question

Proof that $F(a)\approx F[x]/\langle p(x) \rangle$

order of automorphism group and index of finite field extension

show that if $K$ is a field then $K[x]$ is principal

Must an irreducible polynomial over a field extension divide the irreducible polynomial over the subfield?

Can a field with cardinality $3$ be an ordered field?

Is $\mathbb{F}$ an algebraic extension of $k$ if $\dim_k V < |k|$?

What is a Module, and what is an R-module? (understanding the definition)

$\mathbb{Z}[\zeta]$ is not a UFD

Question about the definition of free modules

If there exists a cyclic extension of degree $p$ of $K$, then there exists a cyclic extension of degree $p^n$ for every $n\ge 1$?

field extension Q(∛2) of Q

Example of a nontransitive action of $\operatorname{Aut}(K/\mathbb Q)$ on the roots in $K$ of an irreducible polynomial.

A query about generalizing the complex field

Field Theory: Common root (element of field extension) of two polynomials

Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension

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