Question

When people say, "K is an extension of k with dimension n", do they mean as an algebra or as a vectorspace?

score 85 · Answer 1 · 2014-09-16 23:08:26

85

Views

When people say, "K is an extension of k with dimension n", do they mean as an algebra or as a vectorspace?

Published on 16 Sep 2014 - 23:08

score 83 · Answer 2 · 2026-03-25 05:59:04

83

Views

Is the embedding problem with a cyclic kernel always solvable?

Published on 25 Mar 2026 - 5:59

score 970 · Answer 3 · 2014-09-18 09:12:42

970

Views

What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?

Published on 18 Sep 2014 - 9:12

score 99 · Answer 4 · 2026-03-31 05:41:20

99

Views

Irreducible polynomial with LI roots

Published on 31 Mar 2026 - 5:41

score 1.2k · Answer 5 · 2014-09-18 21:19:29

1.2k

Views

$\mathbf{Q}[\sqrt 5+\sqrt[3] 2]=\mathbf{Q}[\sqrt 5,\sqrt[3] 2]$?

Published on 18 Sep 2014 - 21:19

score 182 · Answer 6 · 2014-09-19 05:26:13

182

Views

$[\mathbb{Q}(\sqrt [3] {2}+\sqrt {5}):\mathbb{Q}]$

Published on 19 Sep 2014 - 5:26

score 93 · Answer 7 · 2014-09-20 14:36:27

93

Views

Find $[\mathbb{Q}(\sqrt [3] {3},\sqrt [3] {2}):\mathbb{Q}]$

Published on 20 Sep 2014 - 14:36

score 112 · Answer 8 · 2014-09-20 20:58:17

112

Views

Let K/F be a transcendental extension , then does every F-homomorphism has to be an automorphism?

Published on 20 Sep 2014 - 20:58

score 886 · Answer 9 · 2026-03-28 06:16:31

886

Views

Field extension of degree 3 and polynomial roots

Published on 28 Mar 2026 - 6:16

score 987 · Answer 10 · 2014-09-25 12:10:50

987

Views

How to Prove: If $A$ and $B$ are subfields of a field $F$, then $\{b+a|b\in B, a\in A\}$ is also a subfield of $F$.

Published on 25 Sep 2014 - 12:10

score 41 · Answer 11 · 2026-03-27 10:10:08

41

Views

Let$\ H$ be a hyperinteger. If$\ f(n)=g(n)$ is true for all$\ n \in \mathbb{N}$, will it be so for all$\ H$?

Published on 27 Mar 2026 - 10:10

score 128 · Answer 12 · 2014-09-28 03:16:46

128

Views

Let $F_\infty=\bigcup_{n\geq1}\operatorname{Q}(2^{1/2^n})$ , $K_\infty=\bigcup_{n\geq1}\operatorname{Q}(\zeta_{2^n})$, what is the intersection?

Published on 28 Sep 2014 - 3:16

score 58 · Answer 13 · 2014-09-29 20:11:57

58

Views

Algebraic Extensions

Published on 29 Sep 2014 - 20:11

score 1.6k · Answer 14 · 2014-09-30 18:03:11

1.6k

Views

$\mathbb{Q}(\sqrt{m}, \sqrt{n})$ : ring of integers, integral basis and discriminant

Published on 30 Sep 2014 - 18:03

score 41 · Answer 15 · 2014-09-30 21:10:02

41

Views

Is every field between $F$ and $F(\alpha_1,\cdots,\alpha_n)$ of the form $F(\alpha_j,\cdots,\alpha_k)$

Published on 30 Sep 2014 - 21:10

List Question

When people say, "K is an extension of k with dimension n", do they mean as an algebra or as a vectorspace?

Is the embedding problem with a cyclic kernel always solvable?

What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?

Irreducible polynomial with LI roots

$\mathbf{Q}[\sqrt 5+\sqrt[3] 2]=\mathbf{Q}[\sqrt 5,\sqrt[3] 2]$?

$[\mathbb{Q}(\sqrt [3] {2}+\sqrt {5}):\mathbb{Q}]$

Find $[\mathbb{Q}(\sqrt [3] {3},\sqrt [3] {2}):\mathbb{Q}]$

Let K/F be a transcendental extension , then does every F-homomorphism has to be an automorphism?

Field extension of degree 3 and polynomial roots

How to Prove: If $A$ and $B$ are subfields of a field $F$, then $\{b+a|b\in B, a\in A\}$ is also a subfield of $F$.

Let$\ H$ be a hyperinteger. If$\ f(n)=g(n)$ is true for all$\ n \in \mathbb{N}$, will it be so for all$\ H$?

Let $F_\infty=\bigcup_{n\geq1}\operatorname{Q}(2^{1/2^n})$ , $K_\infty=\bigcup_{n\geq1}\operatorname{Q}(\zeta_{2^n})$, what is the intersection?

Algebraic Extensions

$\mathbb{Q}(\sqrt{m}, \sqrt{n})$ : ring of integers, integral basis and discriminant

Is every field between $F$ and $F(\alpha_1,\cdots,\alpha_n)$ of the form $F(\alpha_j,\cdots,\alpha_k)$

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