Question

Determine field degree extension of certain number fields.

score 42 · Answer 1 · 2019-02-19 06:28:13

42

Views

Determine field degree extension of certain number fields.

Published on 19 Feb 2019 - 6:28

score 202 · Answer 2 · 2019-02-19 13:40:33

202

Views

$m = [K(\alpha):K], n=[K(\beta):K]$ and $\gcd(m,n)=1$, prove that $K(\alpha + \beta) = K(\alpha,\beta)$

Published on 19 Feb 2019 - 13:40

score 23 · Answer 3 · 2026-03-28 05:57:58

23

Views

When is a field element in its base field?

Published on 28 Mar 2026 - 5:57

score 509 · Answer 4 · 2019-02-19 20:08:08

509

Views

Degree of $\mathbb{Q}(e^{2i\pi / 5}, \sqrt[5]{2}) / \mathbb{Q}$

Published on 19 Feb 2019 - 20:08

score 80 · Answer 5 · 2026-03-25 09:28:11

80

Views

field extension being algebraic is equivalent to every $K-$ algebra being an automorphism.

Published on 25 Mar 2026 - 9:28

score 38 · Answer 6 · 2019-02-20 14:56:14

38

Views

Determine all algebraic extensions of $\Bbb Q$ contained in $\Bbb Q(\sqrt{2},\pi)$

Published on 20 Feb 2019 - 14:56

score 27 · Answer 7 · 2019-02-20 16:39:26

27

Views

Deducing if $\gcd(\deg(m_K(x)),\deg(m_K(y)))=1$ then $[K(x,y):K]=\deg(m_K(x))\times \deg(m_K(y))$.

Published on 20 Feb 2019 - 16:39

score 123 · Answer 8 · 2019-02-20 17:34:26

123

Views

Is there an extension field of degree infinite has no intermediate field?

Published on 20 Feb 2019 - 17:34

score 65 · Answer 9 · 2026-03-25 22:26:05

65

Views

Is $[\Bbb Q(5^{1/2}, 5^{1/7}): \Bbb Q(5^{1/7})]$ a normal extension?

Published on 25 Mar 2026 - 22:26

score 125 · Answer 10 · 2019-02-22 08:31:16

125

Views

About irreducible polynomial over field & characteristic or minimal polynomial of matrix

Published on 22 Feb 2019 - 8:31

score 140 · Answer 11 · 2026-03-26 11:17:41

140

Views

On the existence of an algebraically closed field containing other fields

Published on 26 Mar 2026 - 11:17

score 812 · Answer 12 · 2026-03-28 07:37:16

812

Views

Why is $\mathbb{Z}_3[x]/\langle x^2+1\rangle$ a field with order $9$? And does order $9$ mean it has $9$ elements?

Published on 28 Mar 2026 - 7:37

score 49 · Answer 13 · 2026-03-29 07:00:39

49

Views

Is $\mathbb Q(\sqrt 2) \times \mathbb Q(\sqrt 3)=\mathbb Q(\sqrt 2,\sqrt 3)$ if I prove $\sqrt 2,\sqrt 3$ are L.I. over $\mathbb Q$?

Published on 29 Mar 2026 - 7:00

score 161 · Answer 14 · 2026-03-25 14:27:06

161

Views

Are Valuations on algebraic extensions of an henselian field unique?

Published on 25 Mar 2026 - 14:27

score 359 · Answer 15 · 2026-03-25 21:00:06

359

Views

Can splitting field be generated by one root?

Published on 25 Mar 2026 - 21:00

List Question

Determine field degree extension of certain number fields.

$m = [K(\alpha):K], n=[K(\beta):K]$ and $\gcd(m,n)=1$, prove that $K(\alpha + \beta) = K(\alpha,\beta)$

When is a field element in its base field?

Degree of $\mathbb{Q}(e^{2i\pi / 5}, \sqrt[5]{2}) / \mathbb{Q}$

field extension being algebraic is equivalent to every $K-$ algebra being an automorphism.

Determine all algebraic extensions of $\Bbb Q$ contained in $\Bbb Q(\sqrt{2},\pi)$

Deducing if $\gcd(\deg(m_K(x)),\deg(m_K(y)))=1$ then $[K(x,y):K]=\deg(m_K(x))\times \deg(m_K(y))$.

Is there an extension field of degree infinite has no intermediate field?

Is $[\Bbb Q(5^{1/2}, 5^{1/7}): \Bbb Q(5^{1/7})]$ a normal extension?

About irreducible polynomial over field & characteristic or minimal polynomial of matrix

On the existence of an algebraically closed field containing other fields

Why is $\mathbb{Z}_3[x]/\langle x^2+1\rangle$ a field with order $9$? And does order $9$ mean it has $9$ elements?

Is $\mathbb Q(\sqrt 2) \times \mathbb Q(\sqrt 3)=\mathbb Q(\sqrt 2,\sqrt 3)$ if I prove $\sqrt 2,\sqrt 3$ are L.I. over $\mathbb Q$?

Are Valuations on algebraic extensions of an henselian field unique?

Can splitting field be generated by one root?

Trending Questions

Popular # Hahtags

Popular Questions