Question

Let E be an extension of a field F of degree 2. Show there is an element with $\beta = x^2 - \alpha$

score 710 · Answer 1 · 2015-05-15 19:29:11

710

Views

Let E be an extension of a field F of degree 2. Show there is an element with $\beta = x^2 - \alpha$

Published on 15 May 2015 - 19:29

score 132 · Answer 2 · 2015-05-16 11:24:03

132

Views

Prove $\sigma_g(x) \in Aut(R(x)/R)$

Published on 16 May 2015 - 11:24

score 485 · Answer 3 · 2015-05-16 21:30:04

485

Views

Question on separable field extenions

Published on 16 May 2015 - 21:30

score 1.3k · Answer 4 · 2015-05-17 00:18:04

1.3k

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Show that $K = \mathbb{Q}(\sqrt{p} \ | \ \text{p is prime} \}$ is an algebraic and infinite extension of Q

Published on 17 May 2015 - 0:18

score 57 · Answer 5 · 2015-05-18 15:48:09

57

Views

Prove the form of a fixed field

Published on 18 May 2015 - 15:48

score 359 · Answer 6 · 2026-04-11 17:45:24

359

Views

Field extension over $\mathbb{Q}$

Published on 11 Apr 2026 - 17:45

score 372 · Answer 7 · 2015-05-19 17:57:39

372

Views

Prove that $p(x)$ is irreducible in $F[x]$

Published on 19 May 2015 - 17:57

score 37 · Answer 8 · 2026-04-07 22:59:44

37

Views

Roots of $X^{l-1}+1$ in a quadratic extension $F_q$, $q=l^2$

Published on 07 Apr 2026 - 22:59

score 39 · Answer 9 · 2015-05-20 16:08:01

39

Views

$F(t)$ as an $F[t]$-algebra and the Weak Nullstellensatz

Published on 20 May 2015 - 16:08

score 380 · Answer 10 · 2015-05-21 00:53:30

380

Views

Extension of fields $[L:K]=2$. Show that there is a element $\alpha\in L$ such that $L=K(\alpha)$ and $\alpha^2\in K$.

Published on 21 May 2015 - 0:53

score 205 · Answer 11 · 2015-05-22 01:00:48

Let $K\subseteq F$ be a finite extension of fields, $M$ and $N$ intermediate fields separable on $K$. Show that $MN$ (compositum) is separable.

score 96 · Answer 12 · 2026-04-11 08:37:43

96

Views

Field Theory Problem in Beachy's Abstract Algebra involving field extensions and transcendental elements.

Published on 11 Apr 2026 - 8:37

score 962 · Answer 13 · 2026-04-11 14:45:44

962

Views

Is the degree of an infinite algebraic extensions always countable?

Published on 11 Apr 2026 - 14:45

score 112 · Answer 14 · 2015-05-22 12:21:22

112

Views

Consider extension $[\mathbb{Q}(\alpha\ ):\mathbb{Q}]$ where $\alpha\ $ is zero of $P(x) = x^4 + 9x^{2} + 15 $.

Published on 22 May 2015 - 12:21

score 2.2k · Answer 15 · 2026-03-27 02:07:09

2.2k

Views

How to prove that any infinite algebraic extension of a complete field is never complete?

Published on 27 Mar 2026 - 2:07

List Question

Let E be an extension of a field F of degree 2. Show there is an element with $\beta = x^2 - \alpha$

Prove $\sigma_g(x) \in Aut(R(x)/R)$

Question on separable field extenions

Show that $K = \mathbb{Q}(\sqrt{p} \ | \ \text{p is prime} \}$ is an algebraic and infinite extension of Q

Prove the form of a fixed field

Field extension over $\mathbb{Q}$

Prove that $p(x)$ is irreducible in $F[x]$

Roots of $X^{l-1}+1$ in a quadratic extension $F_q$, $q=l^2$

$F(t)$ as an $F[t]$-algebra and the Weak Nullstellensatz

Extension of fields $[L:K]=2$. Show that there is a element $\alpha\in L$ such that $L=K(\alpha)$ and $\alpha^2\in K$.

Let $K\subseteq F$ be a finite extension of fields, $M$ and $N$ intermediate fields separable on $K$. Show that $MN$ (compositum) is separable.

Field Theory Problem in Beachy's Abstract Algebra involving field extensions and transcendental elements.

Is the degree of an infinite algebraic extensions always countable?

Consider extension $[\mathbb{Q}(\alpha\ ):\mathbb{Q}]$ where $\alpha\ $ is zero of $P(x) = x^4 + 9x^{2} + 15 $.

How to prove that any infinite algebraic extension of a complete field is never complete?

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