Question

powers in field extension

score 41 · Answer 1 · 2026-04-10 23:47:19

41

Views

powers in field extension

Published on 10 Apr 2026 - 23:47

score 63 · Answer 2 · 2026-04-16 08:09:47

63

Views

Need to show $K(\alpha,\beta)$ is not a simple extension of $K(\alpha^p,\beta^p)$

Published on 16 Apr 2026 - 8:09

score 28 · Answer 3 · 2026-04-16 05:29:37

28

Views

Find all values of the positive integer $n$ such that $Q(e^{\frac {2πi}{n}})$ contains $i.$

Published on 16 Apr 2026 - 5:29

score 52 · Answer 4 · 2026-04-15 02:48:08

52

Views

$L|_k$ be a finite Galois extension and $M,N$ are subfields containing $k$ such that $[M:k], [N:k]$ are powers of $2$. Is $[MN:k]$ power of $2$?

Published on 15 Apr 2026 - 2:48

score 99 · Answer 5 · 2026-04-15 19:05:17

99

Views

Is $\mathbb{Q}(\alpha^8)=\mathbb{Q}(\alpha)$?

Published on 15 Apr 2026 - 19:05

score 180 · Answer 6 · 2026-04-15 04:00:32

180

Views

Show that $x^{21}+2x^8+1$ does not have multiple zeroes in any extension of $Z_3$.

Published on 15 Apr 2026 - 4:00

score 82 · Answer 7 · 2026-04-10 13:45:34

82

Views

Computing a certain Galois group

Published on 10 Apr 2026 - 13:45

score 33 · Answer 8 · 2026-04-14 20:19:50

33

Views

Condition for guarantee f and f' relative primes over a polynomial ring.

Published on 14 Apr 2026 - 20:19

score 167 · Answer 9 · 2026-04-15 21:20:11

167

Views

$L$ be an algebraically closed field and $\sigma \in \operatorname{Aut}(L)$, if $F=L^{\sigma}$, then every finite extension $E/F$ is cyclic.

Published on 15 Apr 2026 - 21:20

score 70 · Answer 10 · 2026-04-12 10:21:46

70

Views

Two elements are not equal by using algebraic independent trick

Published on 12 Apr 2026 - 10:21

score 88 · Answer 11 · 2026-04-12 14:35:26

88

Views

$\frac{1}{n}$ does not converge to $0$ in $\mathbb{R}(t)$?

Published on 12 Apr 2026 - 14:35

score 219 · Answer 12 · 2026-04-17 03:43:32

219

Views

Prove $Q_{mp} = Q_{m}(x^p)$ when prime $p$ divides $m$. ($Q$ is cyclotomic polynomial over some finite field $K$)

Published on 17 Apr 2026 - 3:43

score 737 · Answer 13 · 2026-04-15 13:44:00

737

Views

Prove that a field is a vector space over a subfield

Published on 15 Apr 2026 - 13:44

score 84 · Answer 14 · 2026-04-12 06:27:41

84

Views

Not surjective function by using algebra tools

Published on 12 Apr 2026 - 6:27

score 119 · Answer 15 · 2026-04-10 18:29:45

119

Views

Splitting field of a polynomial of degree 6

Published on 10 Apr 2026 - 18:29

List Question

powers in field extension

Need to show $K(\alpha,\beta)$ is not a simple extension of $K(\alpha^p,\beta^p)$

Find all values of the positive integer $n$ such that $Q(e^{\frac {2πi}{n}})$ contains $i.$

$L|_k$ be a finite Galois extension and $M,N$ are subfields containing $k$ such that $[M:k], [N:k]$ are powers of $2$. Is $[MN:k]$ power of $2$?

Is $\mathbb{Q}(\alpha^8)=\mathbb{Q}(\alpha)$?

Show that $x^{21}+2x^8+1$ does not have multiple zeroes in any extension of $Z_3$.

Computing a certain Galois group

Condition for guarantee f and f' relative primes over a polynomial ring.

$L$ be an algebraically closed field and $\sigma \in \operatorname{Aut}(L)$, if $F=L^{\sigma}$, then every finite extension $E/F$ is cyclic.

Two elements are not equal by using algebraic independent trick

$\frac{1}{n}$ does not converge to $0$ in $\mathbb{R}(t)$?

Prove $Q_{mp} = Q_{m}(x^p)$ when prime $p$ divides $m$. ($Q$ is cyclotomic polynomial over some finite field $K$)

Prove that a field is a vector space over a subfield

Not surjective function by using algebra tools

Splitting field of a polynomial of degree 6

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