Question

Show that Q[x] /(x^2-2) is not isomorphic to Q[x] /(x^2-3)

score 911 · Answer 1 · 2026-04-17 13:55:44

911

Views

Show that Q[x] /(x^2-2) is not isomorphic to Q[x] /(x^2-3)

Published on 17 Apr 2026 - 13:55

score 1.2k · Answer 2 · 2026-04-14 23:32:52

1.2k

Views

Galois group of $P(X) = X^5 -7$

Published on 14 Apr 2026 - 23:32

score 580 · Answer 3 · 2026-04-14 20:08:11

580

Views

Find the degree of splitting field of $x^3-x+1$ over $\mathbb{F_3}$

Published on 14 Apr 2026 - 20:08

score 76 · Answer 4 · 2026-04-15 22:06:09

76

Views

Show that $\mathbb{F}(a,b) = \mathbb{F}(b,a)$, what is $\mathbb{F}$? A field? What are $a,b$?

Published on 15 Apr 2026 - 22:06

score 237 · Answer 5 · 2026-04-24 14:29:43

237

Views

Extension field notation

Published on 24 Apr 2026 - 14:29

score 41 · Answer 6 · 2026-04-12 22:22:44

41

Views

Infinite trascendence degree implies existence of a homomorphism

Published on 12 Apr 2026 - 22:22

score 559 · Answer 7 · 2026-04-16 05:01:07

559

Views

Determine whether the following fields are Galois over $\mathbb{Q}$.

Published on 16 Apr 2026 - 5:01

score 2.2k · Answer 8 · 2026-04-16 14:21:08

2.2k

Views

If $F\subseteq L\subseteq K$ are fields with $K/L$ and $L/F$ Galois, then $K/F$ is Galois?.

Published on 16 Apr 2026 - 14:21

score 689 · Answer 9 · 2026-04-14 18:23:17

689

Views

Let $k$ be a field, and let $K = k(x)$ be the rational function field in one variable over $k$. Let $\sigma$ and $\tau$ be the automorphisms of $K$

Published on 14 Apr 2026 - 18:23

score 2k · Answer 10 · 2026-04-15 05:02:24

2k

Views

$a$ algebraic number, $\exists$ integer $n>0$ such that $na$ algebraic integer

Published on 15 Apr 2026 - 5:02

score 39 · Answer 11 · 2026-04-17 00:42:16

39

Views

Show that $\mathbb{F}(w)$ is the splitting field of $x^4+x^2+1$, $w = (-1+i\sqrt{3})/2$

Published on 17 Apr 2026 - 0:42

score 42 · Answer 12 · 2026-03-26 08:03:32

42

Views

Mapping of Field Extensions of Prime power

Published on 26 Mar 2026 - 8:03

score 92 · Answer 13 · 2026-04-14 07:09:45

92

Views

Give an example of fields $k\subseteq K\subseteq L $, and $l\subseteq L$, for which $l/k$ and $L/K$ are algebraic, $k$ is algebraically closed

Published on 14 Apr 2026 - 7:09

score 114 · Answer 14 · 2026-04-16 19:42:01

114

Views

$L=\mathbb{Q}(\alpha,\beta)$ such that $\alpha^3 + \alpha + 1 = 0$ and $\beta^2 + \beta -3 = 0$. Find $[L:\mathbb{Q}]$

Published on 16 Apr 2026 - 19:42

score 76 · Answer 15 · 2026-04-15 18:31:11

76

Views

Does there always exist an automorphism in $Gal(E/ℚ(x_1))$ besides the indentity?

Published on 15 Apr 2026 - 18:31

List Question

Show that Q[x] /(x^2-2) is not isomorphic to Q[x] /(x^2-3)

Galois group of $P(X) = X^5 -7$

Find the degree of splitting field of $x^3-x+1$ over $\mathbb{F_3}$

Show that $\mathbb{F}(a,b) = \mathbb{F}(b,a)$, what is $\mathbb{F}$? A field? What are $a,b$?

Extension field notation

Infinite trascendence degree implies existence of a homomorphism

Determine whether the following fields are Galois over $\mathbb{Q}$.

If $F\subseteq L\subseteq K$ are fields with $K/L$ and $L/F$ Galois, then $K/F$ is Galois?.

Let $k$ be a field, and let $K = k(x)$ be the rational function field in one variable over $k$. Let $\sigma$ and $\tau$ be the automorphisms of $K$

$a$ algebraic number, $\exists$ integer $n>0$ such that $na$ algebraic integer

Show that $\mathbb{F}(w)$ is the splitting field of $x^4+x^2+1$, $w = (-1+i\sqrt{3})/2$

Mapping of Field Extensions of Prime power

Give an example of fields $k\subseteq K\subseteq L $, and $l\subseteq L$, for which $l/k$ and $L/K$ are algebraic, $k$ is algebraically closed

$L=\mathbb{Q}(\alpha,\beta)$ such that $\alpha^3 + \alpha + 1 = 0$ and $\beta^2 + \beta -3 = 0$. Find $[L:\mathbb{Q}]$

Does there always exist an automorphism in $Gal(E/ℚ(x_1))$ besides the indentity?

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