Question

Why does $\lvert \Bbb{Q} [\sqrt[n]{2}] : \Bbb{Q} \rvert = n$ if $ \Bbb{Q} [\sqrt[n]{2}]$ is formed by adding only one element?

score 75 · Answer 1 · 2026-04-17 15:29:55

75

Views

Why does $\lvert \Bbb{Q} [\sqrt[n]{2}] : \Bbb{Q} \rvert = n$ if $ \Bbb{Q} [\sqrt[n]{2}]$ is formed by adding only one element?

Published on 17 Apr 2026 - 15:29

score 92 · Answer 2 · 2026-04-15 09:22:17

92

Views

Intersection of rational functions subfields must be the scalar field

Published on 15 Apr 2026 - 9:22

score 57 · Answer 3 · 2026-04-14 07:32:23

57

Views

How to see the fact that $\zeta_{p^2}$ is a root of $x^{p(p-1)}+x^{p(p-2)}+...+x^{2p}+x^p+1$?

Published on 14 Apr 2026 - 7:32

score 63 · Answer 4 · 2026-04-11 06:17:12

63

Views

Question about the numbers of distinct roots of a polynomial

Published on 11 Apr 2026 - 6:17

score 39 · Answer 5 · 2026-04-13 07:19:21

39

Views

Question about separable extension

Published on 13 Apr 2026 - 7:19

score 93 · Answer 6 · 2026-04-14 23:31:21

93

Views

(From Milne's field theory notes)Why does the splitting field of a degree-$3$ irreduciblle polynomial has degree $3$ or $6$ over $\Bbb Q$?

Published on 14 Apr 2026 - 23:31

score 34 · Answer 7 · 2026-04-11 05:22:52

34

Views

Field extensions and irreducible polynomials

Published on 11 Apr 2026 - 5:22

score 131 · Answer 8 · 2026-03-29 14:07:10

131

Views

Prove an field extension to be Galois

Published on 29 Mar 2026 - 14:07

score 35 · Answer 9 · 2026-04-14 03:11:03

35

Views

What is the value of $ \ n\ $ such that $\ \xi_{n}= e^{\frac{2 \pi i}{n}} \ $

Published on 14 Apr 2026 - 3:11

score 319 · Answer 10 · 2026-04-16 05:22:28

319

Views

If $\alpha^2$ is algebraic over $F$ then $\alpha$ is algebraic over $F$.

Published on 16 Apr 2026 - 5:22

score 127 · Answer 11 · 2026-04-14 14:36:26

127

Views

Intersection of Simple Extensions

Published on 14 Apr 2026 - 14:36

score 722 · Answer 12 · 2026-04-15 22:38:42

722

Views

Intermediate fields of $x^4+1$

Published on 15 Apr 2026 - 22:38

score 442 · Answer 13 · 2026-04-09 15:36:27

442

Views

Understanding solvability by radicals

Published on 09 Apr 2026 - 15:36

score 142 · Answer 14 · 2026-04-11 15:00:52

142

Views

How can I see that $\Bbb F_{p^2}(t)$ is a separable extension of $\Bbb F_p(t)$?

Published on 11 Apr 2026 - 15:00

score 462 · Answer 15 · 2026-04-15 08:40:09

462

Views

Galois extension of $\mathbb{Q}(i)$ with Galois group $D_8$

Published on 15 Apr 2026 - 8:40

List Question

Why does $\lvert \Bbb{Q} [\sqrt[n]{2}] : \Bbb{Q} \rvert = n$ if $ \Bbb{Q} [\sqrt[n]{2}]$ is formed by adding only one element?

Intersection of rational functions subfields must be the scalar field

How to see the fact that $\zeta_{p^2}$ is a root of $x^{p(p-1)}+x^{p(p-2)}+...+x^{2p}+x^p+1$?

Question about the numbers of distinct roots of a polynomial

Question about separable extension

(From Milne's field theory notes)Why does the splitting field of a degree-$3$ irreduciblle polynomial has degree $3$ or $6$ over $\Bbb Q$?

Field extensions and irreducible polynomials

Prove an field extension to be Galois

What is the value of $ \ n\ $ such that $\ \xi_{n}= e^{\frac{2 \pi i}{n}} \ $

If $\alpha^2$ is algebraic over $F$ then $\alpha$ is algebraic over $F$.

Intersection of Simple Extensions

Intermediate fields of $x^4+1$

Understanding solvability by radicals

How can I see that $\Bbb F_{p^2}(t)$ is a separable extension of $\Bbb F_p(t)$?

Galois extension of $\mathbb{Q}(i)$ with Galois group $D_8$

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