Question

Is it possible to get the same extension field E/F of F by using different homomorphisms?

score 54 · Answer 1 · 2026-03-26 04:34:03

54

Views

Is it possible to get the same extension field E/F of F by using different homomorphisms?

Published on 26 Mar 2026 - 4:34

score 100 · Answer 2 · 2017-03-11 13:59:33

100

Views

$M/F$ is not simple

Published on 11 Mar 2017 - 13:59

score 93 · Answer 3 · 2026-03-27 06:17:12

93

Views

One zero in extension field $F$ implies other zero in $F$

Published on 27 Mar 2026 - 6:17

score 1.1k · Answer 4 · 2017-03-12 07:20:33

1.1k

Views

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

Published on 12 Mar 2017 - 7:20

score 555 · Answer 5 · 2017-03-12 11:18:26

555

Views

order of automorphism group and index of finite field extension

Published on 12 Mar 2017 - 11:18

score 117 · Answer 6 · 2017-03-12 16:27:09

117

Views

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

Published on 12 Mar 2017 - 16:27

score 62 · Answer 7 · 2017-03-12 16:48:16

62

Views

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

Published on 12 Mar 2017 - 16:48

score 244 · Answer 8 · 2017-03-13 06:29:51

244

Views

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

Published on 13 Mar 2017 - 6:29

score 118 · Answer 9 · 2017-03-13 10:43:02

118

Views

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

Published on 13 Mar 2017 - 10:43

score 2.4k · Answer 10 · 2017-03-13 13:22:55

2.4k

Views

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

Published on 13 Mar 2017 - 13:22

score 56 · Answer 11 · 2026-03-27 06:17:10

56

Views

Understanding this theorem indicating the simplicity of a field extension

Published on 27 Mar 2026 - 6:17

score 167 · Answer 12 · 2017-03-14 03:16:00

167

Views

normal and separable extension

Published on 14 Mar 2017 - 3:16

score 339 · Answer 13 · 2017-03-15 08:19:31

339

Views

Is this field extension finite?

Published on 15 Mar 2017 - 8:19

score 2k · Answer 14 · 2026-04-03 03:36:56

2k

Views

Write $x^3 + 2x+1$ as a product of linear polynomials over some extension field of $\mathbb{Z}_3$

Published on 03 Apr 2026 - 3:36

score 320 · Answer 15 · 2026-04-03 03:36:58

320

Views

Specific proof of irreducibility of $X^2-3$ in $\mathbb{Q}(\sqrt{2})[X]$

Published on 03 Apr 2026 - 3:36

List Question

Is it possible to get the same extension field E/F of F by using different homomorphisms?

$M/F$ is not simple

One zero in extension field $F$ implies other zero in $F$

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

order of automorphism group and index of finite field extension

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

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

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

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

Understanding this theorem indicating the simplicity of a field extension

normal and separable extension

Is this field extension finite?

Write $x^3 + 2x+1$ as a product of linear polynomials over some extension field of $\mathbb{Z}_3$

Specific proof of irreducibility of $X^2-3$ in $\mathbb{Q}(\sqrt{2})[X]$

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