Question

Finite field extension proposition - need explanation

score 115 · Answer 1 · 2017-02-03 01:11:40

115

Views

Finite field extension proposition - need explanation

Published on 03 Feb 2017 - 1:11

score 534 · Answer 2 · 2017-02-03 14:04:31

534

Views

Is $\Bbb C$ a purely transcendental extension of a proper subfield?

Published on 03 Feb 2017 - 14:04

score 129 · Answer 3 · 2026-03-26 03:11:21

129

Views

Any linear combination of $\{a_1,a_2,\cdots,a_n\}$ is also separable over $K$

Published on 26 Mar 2026 - 3:11

score 431 · Answer 4 · 2017-02-05 20:40:14

431

Views

Transcendental element and algebraic closure

Published on 05 Feb 2017 - 20:40

score 41 · Answer 5 · 2017-02-06 02:57:55

41

Views

What is meant by $F(\beta )$ in field theory?

Published on 06 Feb 2017 - 2:57

score 50 · Answer 6 · 2017-02-06 08:48:21

50

Views

Is it true that the field $E$ which contains all $p^r$th roots of elements of a field $F$ is perfect?

Published on 06 Feb 2017 - 8:48

score 38 · Answer 7 · 2017-02-06 21:28:28

38

Views

Algebraic closures of subextensions are all the same?

Published on 06 Feb 2017 - 21:28

score 841 · Answer 8 · 2017-02-07 14:24:06

841

Views

If α is algebraic over F then F(α) is algebraic over F

Published on 07 Feb 2017 - 14:24

score 1.3k · Answer 9 · 2017-02-08 05:12:36

1.3k

Views

Show if $\alpha$ is algebraic over $F$, then $\alpha ^2$ is algebraic over $F$

Published on 08 Feb 2017 - 5:12

score 50 · Answer 10 · 2017-02-08 05:28:00

50

Views

Proving that $\mathbb{Q}(\sqrt{p_1}) \ne \mathbb{Q}(\sqrt{p_2})$

Published on 08 Feb 2017 - 5:28

score 77 · Answer 11 · 2017-02-08 14:28:28

77

Views

Minimal polynomial of $\frac{\sqrt{5}+1}{2}$

Published on 08 Feb 2017 - 14:28

score 350 · Answer 12 · 2026-04-02 23:01:48

350

Views

Show that $f(x)=x^4-4x^2+8x+2$ is irreducible in $K=\mathbb Q(\sqrt 2 i)$.

Published on 02 Apr 2026 - 23:01

score 265 · Answer 13 · 2017-02-11 11:32:26

265

Views

Fixed field is a field

Published on 11 Feb 2017 - 11:32

score 56 · Answer 14 · 2026-04-04 07:56:35

56

Views

Let $E_1$ and $E_2$ be two extension of a field $F$ and $[E_2:F]=2$ such that $E_1\cap E_2=F$.Let $E_2=F(\alpha)$ then $[E_1(\alpha):E_1]?$

Published on 04 Apr 2026 - 7:56

score 463 · Answer 15 · 2017-02-12 07:59:57

463

Views

If extension $E/F$ has degree $2$, how can we show that $E=F(\alpha)$ where $\alpha$ is a root of $t^2 - b$, $b \in F$? ($F$ in characteristic $0$)

Published on 12 Feb 2017 - 7:59

List Question

Finite field extension proposition - need explanation

Is $\Bbb C$ a purely transcendental extension of a proper subfield?

Any linear combination of $\{a_1,a_2,\cdots,a_n\}$ is also separable over $K$

Transcendental element and algebraic closure

What is meant by $F(\beta )$ in field theory?

Is it true that the field $E$ which contains all $p^r$th roots of elements of a field $F$ is perfect?

Algebraic closures of subextensions are all the same?

If α is algebraic over F then F(α) is algebraic over F

Show if $\alpha$ is algebraic over $F$, then $\alpha ^2$ is algebraic over $F$

Proving that $\mathbb{Q}(\sqrt{p_1}) \ne \mathbb{Q}(\sqrt{p_2})$

Minimal polynomial of $\frac{\sqrt{5}+1}{2}$

Show that $f(x)=x^4-4x^2+8x+2$ is irreducible in $K=\mathbb Q(\sqrt 2 i)$.

Fixed field is a field

Let $E_1$ and $E_2$ be two extension of a field $F$ and $[E_2:F]=2$ such that $E_1\cap E_2=F$.Let $E_2=F(\alpha)$ then $[E_1(\alpha):E_1]?$

If extension $E/F$ has degree $2$, how can we show that $E=F(\alpha)$ where $\alpha$ is a root of $t^2 - b$, $b \in F$? ($F$ in characteristic $0$)

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