Question

Combining two field extensions?

score 31 · Answer 1 · 2026-04-11 13:44:39

31

Views

Combining two field extensions?

Published on 11 Apr 2026 - 13:44

score 39 · Answer 2 · 2026-04-16 17:48:03

39

Views

If $[E:F] = n$, $m < n$ show that there cannot be an injective F-algebra homomorphism $L:E \rightarrow M(m, F)$.

Published on 16 Apr 2026 - 17:48

score 268 · Answer 3 · 2026-04-13 04:21:08

268

Views

Fixed field is a field

Published on 13 Apr 2026 - 4:21

score 40 · Answer 4 · 2026-04-15 19:06:43

40

Views

For arbitrary group G of automorphisms of K, $ord(G)=[K :K_G]$?

Published on 15 Apr 2026 - 19:06

score 39 · Answer 5 · 2026-04-16 04:56:59

39

Views

H is a group with p $\epsilon \hspace{0,1 cm} \mathbb{P}$ elements (Ord(H) = p $\epsilon \hspace{0,1 cm} \mathbb{P}$) . Determine all sub groups of H.

Published on 16 Apr 2026 - 4:56

score 57 · Answer 6 · 2026-04-15 14:18:39

57

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 15 Apr 2026 - 14:18

score 500 · Answer 7 · 2026-04-14 15:56:16

500

Views

Name for a polynomial where adjoining one root is Galois

Published on 14 Apr 2026 - 15:56

score 466 · Answer 8 · 2026-04-16 08:23:35

466

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 16 Apr 2026 - 8:23

score 501 · Answer 9 · 2026-04-17 03:53:49

501

Views

Separability of $x^p-t$ over field of rational functions $\mathbb{F}_p(t)$

Published on 17 Apr 2026 - 3:53

score 1k · Answer 10 · 2026-04-14 16:57:18

1k

Views

If $E/F$ and $F/k$ are algebraic extensions then $E/k$ is also algebraic.

Published on 14 Apr 2026 - 16:57

score 561 · Answer 11 · 2026-04-08 16:18:08

561

Views

Degree of splitting field?

Published on 08 Apr 2026 - 16:18

score 1.1k · Answer 12 · 2026-04-16 14:30:43

1.1k

Views

Automorphism of $\mathbb Q(\cos(2\pi/n))$

Published on 16 Apr 2026 - 14:30

score 162 · Answer 13 · 2026-04-16 13:30:42

162

Views

Decomposition and inerta fields in $\mathbb{Q}(\zeta_{12})$

Published on 16 Apr 2026 - 13:30

score 161 · Answer 14 · 2026-04-11 06:27:41

161

Views

Extension $L/K$ with specific decomposition properties

Published on 11 Apr 2026 - 6:27

score 1k · Answer 15 · 2026-04-10 23:46:53

1k

Views

What does it mean to be an irreducible polynomial over a field? (need clarification on the definition)

Published on 10 Apr 2026 - 23:46

List Question

Combining two field extensions?

If $[E:F] = n$, $m < n$ show that there cannot be an injective F-algebra homomorphism $L:E \rightarrow M(m, F)$.

Fixed field is a field

For arbitrary group G of automorphisms of K, $ord(G)=[K :K_G]$?

H is a group with p $\epsilon \hspace{0,1 cm} \mathbb{P}$ elements (Ord(H) = p $\epsilon \hspace{0,1 cm} \mathbb{P}$) . Determine all sub groups of H.

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 $[E_1(\alpha):E_1]?$

Name for a polynomial where adjoining one root is Galois

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 $0$)

Separability of $x^p-t$ over field of rational functions $\mathbb{F}_p(t)$

If $E/F$ and $F/k$ are algebraic extensions then $E/k$ is also algebraic.

Degree of splitting field?

Automorphism of $\mathbb Q(\cos(2\pi/n))$

Decomposition and inerta fields in $\mathbb{Q}(\zeta_{12})$

Extension $L/K$ with specific decomposition properties

What does it mean to be an irreducible polynomial over a field? (need clarification on the definition)

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