Question

$k \subseteq K$ be a field extension with $[K:k] = p$ prime, $f(X) \in k[x]$ with $\deg{f(X)} = p + 1$. $f$ has a root in $K$ iff has a root in $k$.

score 33 · Answer 1 · 2026-04-14 22:59:14

33

Views

$k \subseteq K$ be a field extension with $[K:k] = p$ prime, $f(X) \in k[x]$ with $\deg{f(X)} = p + 1$. $f$ has a root in $K$ iff has a root in $k$.

Published on 14 Apr 2026 - 22:59

score 589 · Answer 2 · 2026-04-16 04:51:50

589

Views

What is the characteristics polynomial of some element of the extended field over the base field?

Published on 16 Apr 2026 - 4:51

score 290 · Answer 3 · 2026-04-17 01:09:05

290

Views

$\mathbb{Q}(\sqrt{p^*})$ is the only quadratic extension of $\mathbb{Q}$ contained in $\mathbb{Q}(\zeta_{p^n})$.

Published on 17 Apr 2026 - 1:09

score 61 · Answer 4 · 2026-04-15 22:19:56

61

Views

Polynomial in $\mathbb{F}_{q}$

Published on 15 Apr 2026 - 22:19

score 40 · Answer 5 · 2019-10-14 15:43:10

40

Views

Can we say that $m_{T_y} = m_y$?

Published on 14 Oct 2019 - 15:43

score 233 · Answer 6 · 2026-04-12 15:19:42

233

Views

Frobenius element of unramified extension

Published on 12 Apr 2026 - 15:19

score 32 · Answer 7 · 2026-04-16 11:04:09

32

Views

Isomorphism between algebraic extensions and irreducible polynomials

Published on 16 Apr 2026 - 11:04

score 180 · Answer 8 · 2026-04-14 23:48:32

180

Views

Does $\sqrt{3-\sqrt{3}} \in \mathbb{Q}(\sqrt{3+\sqrt{3}})$?

Published on 14 Apr 2026 - 23:48

score 807 · Answer 9 · 2026-04-17 10:58:41

807

Views

Inverse element of $x^2 + x + 1$ in $\mathbb Z_2[x]/\langle x^3 + x + 1\rangle$

Published on 17 Apr 2026 - 10:58

score 89 · Answer 10 · 2026-04-15 21:05:53

89

Views

Prove that $\chi_y = \prod\limits_{\sigma \in G} \left (X-\sigma(y) \right ).$

Published on 15 Apr 2026 - 21:05

score 98 · Answer 11 · 2026-04-09 19:05:23

98

Views

Lack of Basic Understanding about Linear Algebra/ Field Theory

Published on 09 Apr 2026 - 19:05

score 473 · Answer 12 · 2026-04-16 01:28:52

473

Views

Is $\mathbb{C}[x,y]/\langle x^2+y^2\rangle$ a field?

Published on 16 Apr 2026 - 1:28

score 32 · Answer 13 · 2026-04-11 15:06:06

32

Views

What are the multiplicative inverses for K(n)?

Published on 11 Apr 2026 - 15:06

score 39 · Answer 14 · 2026-04-09 05:29:47

39

Views

Finding $a,b \in k$ such that $\gcd(f(t)-a,g(t)-b)=t$

Published on 09 Apr 2026 - 5:29

score 37 · Answer 15 · 2026-04-13 14:55:02

37

Views

Question about Associates in $\mathbb Q$

Published on 13 Apr 2026 - 14:55

List Question

$k \subseteq K$ be a field extension with $[K:k] = p$ prime, $f(X) \in k[x]$ with $\deg{f(X)} = p + 1$. $f$ has a root in $K$ iff has a root in $k$.

What is the characteristics polynomial of some element of the extended field over the base field?

$\mathbb{Q}(\sqrt{p^*})$ is the only quadratic extension of $\mathbb{Q}$ contained in $\mathbb{Q}(\zeta_{p^n})$.

Polynomial in $\mathbb{F}_{q}$

Can we say that $m_{T_y} = m_y$?

Frobenius element of unramified extension

Isomorphism between algebraic extensions and irreducible polynomials

Does $\sqrt{3-\sqrt{3}} \in \mathbb{Q}(\sqrt{3+\sqrt{3}})$?

Inverse element of $x^2 + x + 1$ in $\mathbb Z_2[x]/\langle x^3 + x + 1\rangle$

Prove that $\chi_y = \prod\limits_{\sigma \in G} \left (X-\sigma(y) \right ).$

Lack of Basic Understanding about Linear Algebra/ Field Theory

Is $\mathbb{C}[x,y]/\langle x^2+y^2\rangle$ a field?

What are the multiplicative inverses for K(n)?

Finding $a,b \in k$ such that $\gcd(f(t)-a,g(t)-b)=t$

Question about Associates in $\mathbb Q$

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