Question

Show that the algebraic closure of $F$ in $K$ is an algebraic closure of $F$.

score 1.1k · Answer 1 · 2026-04-15 11:14:52

1.1k

Views

Show that the algebraic closure of $F$ in $K$ is an algebraic closure of $F$.

Published on 15 Apr 2026 - 11:14

score 530 · Answer 2 · 2026-05-10 12:53:33

530

Views

Uniqueness of group given only group presentation

Published on 10 May 2026 - 12:53

score 44 · Answer 3 · 2026-04-15 18:53:15

44

Views

If $p(a,b)=0$ where $a,b \in \mathbb R$ then $p(x,y)=(x-a)s(x,y) + (y-b)t(x,y)$ for polynomials $s$ and $t$.

Published on 15 Apr 2026 - 18:53

score 304 · Answer 4 · 2026-05-11 09:09:08

304

Views

Show that $G$ is isomorphic to $\operatorname{Aut}_{G-Set}(G)$

Published on 11 May 2026 - 9:09

score 92 · Answer 5 · 2026-05-07 11:49:03

92

Views

Prove this field extension is separable

Published on 07 May 2026 - 11:49

score 45 · Answer 6 · 2026-04-15 18:08:19

45

Views

Fix(Gal($\bar{F}/F)) = F$ when $\bar{F}$ is separable over $F$

Published on 15 Apr 2026 - 18:08

score 72 · Answer 7 · 2026-05-11 04:36:16

72

Views

Decomposition of $\mathbb{Q}(\sqrt {2}) \otimes \mathbb{Q}(\sqrt {i}) $

Published on 11 May 2026 - 4:36

score 71 · Answer 8 · 2026-04-10 20:20:47

71

Views

Advantages of using negative number in modulo operation?

Published on 10 Apr 2026 - 20:20

score 2.5k · Answer 9 · 2026-04-16 14:49:32

2.5k

Views

Let $f(x)$ be an irreducible polynomial over $F$ of degree $n$, and let $K$ be a field extension of $F$ with $[K:F]=m$

Published on 16 Apr 2026 - 14:49

score 205 · Answer 10 · 2026-05-10 15:10:24

205

Views

What do you mean by splitting field? Find the splitting field of $x^5 -1$

Published on 10 May 2026 - 15:10

score 2.1k · Answer 11 · 2026-04-14 11:34:43

2.1k

Views

Determine the splitting field of $x^4 - 7$ over

Published on 14 Apr 2026 - 11:34

score 288 · Answer 12 · 2026-04-14 22:15:34

288

Views

Element of certain order in multiplicative group

Published on 14 Apr 2026 - 22:15

score 121 · Answer 13 · 2026-04-14 13:02:52

121

Views

Existence of Polynomial with whom product contains only prime powers

Published on 14 Apr 2026 - 13:02

score 237 · Answer 14 · 2026-05-10 17:38:39

237

Views

How to find elements by which 2 elements of $S_n$ are conjugate to each other?

Published on 10 May 2026 - 17:38

score 126 · Answer 15 · 2026-05-11 00:30:45

126

Views

Matrix ring over a semi-simple algebra

Published on 11 May 2026 - 0:30

List Question

Show that the algebraic closure of $F$ in $K$ is an algebraic closure of $F$.

Uniqueness of group given only group presentation

If $p(a,b)=0$ where $a,b \in \mathbb R$ then $p(x,y)=(x-a)s(x,y) + (y-b)t(x,y)$ for polynomials $s$ and $t$.

Show that $G$ is isomorphic to $\operatorname{Aut}_{G-Set}(G)$

Prove this field extension is separable

Fix(Gal($\bar{F}/F)) = F$ when $\bar{F}$ is separable over $F$

Decomposition of $\mathbb{Q}(\sqrt {2}) \otimes \mathbb{Q}(\sqrt {i}) $

Advantages of using negative number in modulo operation?

Let $f(x)$ be an irreducible polynomial over $F$ of degree $n$, and let $K$ be a field extension of $F$ with $[K:F]=m$

What do you mean by splitting field? Find the splitting field of $x^5 -1$

Determine the splitting field of $x^4 - 7$ over

Element of certain order in multiplicative group

Existence of Polynomial with whom product contains only prime powers

How to find elements by which 2 elements of $S_n$ are conjugate to each other?

Matrix ring over a semi-simple algebra

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