Question

What is the meaning of the notation $x\in K, x^{\rho\circ\sigma}$ where $\rho\in \operatorname{Aut}(K),\sigma:K\to\mathbb C$

score 113 · Answer 1 · 2026-04-14 21:14:33

113

Views

What is the meaning of the notation $x\in K, x^{\rho\circ\sigma}$ where $\rho\in \operatorname{Aut}(K),\sigma:K\to\mathbb C$

Published on 14 Apr 2026 - 21:14

score 213 · Answer 2 · 2026-04-15 03:03:46

213

Views

A finite ring of matrices is a finite field

Published on 15 Apr 2026 - 3:03

score 117 · Answer 3 · 2026-04-17 21:06:48

117

Views

Vector space basis theorem, can it be generalized to R-modules?

Published on 17 Apr 2026 - 21:06

score 316 · Answer 4 · 2026-04-17 09:36:15

316

Views

$\mathbb Q(\sqrt{2},i)=\mathbb Q(\sqrt{-2},i)$

Published on 17 Apr 2026 - 9:36

score 236 · Answer 5 · 2026-04-16 09:38:34

236

Views

$Norm_{(\mathbb Q(\zeta_p)|\mathbb Q)}(1-\zeta_p)=p$

Published on 16 Apr 2026 - 9:38

score 81 · Answer 6 · 2026-04-15 17:23:47

81

Views

$K=F(\alpha)$ if $K$ is a quadratic extension

Published on 15 Apr 2026 - 17:23

score 216 · Answer 7 · 2026-04-16 03:55:25

216

Views

Corollary 15.3.8 from Artin (degrees of field extensions)

Published on 16 Apr 2026 - 3:55

score 47 · Answer 8 · 2026-04-16 04:17:57

Showing that if $F,G \in k[x_1, ..., x_n]$ are two polynomials such that $V(F,G)$ is irreducible, that dim$(V(F,G))$ does not have to be $n - 2$

score 613 · Answer 9 · 2026-04-19 21:43:48

613

Views

How to show that if p is prime and m,n are natural numbers then $p^m -1 | p^n -1$

Published on 19 Apr 2026 - 21:43

score 287 · Answer 10 · 2026-04-10 21:14:01

287

Views

Weird Invariant of Finite Reflection Groups

Published on 10 Apr 2026 - 21:14

score 218 · Answer 11 · 2026-04-14 14:14:33

218

Views

How to know under multiplication modulo operation the set is closed or not

Published on 14 Apr 2026 - 14:14

score 181 · Answer 12 · 2026-04-14 22:02:45

181

Views

Proving $\mathbb{Q}(r)$ is Galois over $\mathbb{Q}$ ?

Published on 14 Apr 2026 - 22:02

score 155 · Answer 13 · 2026-04-25 04:48:22

155

Views

Is the intersection of two subgroups, defined below, always trivial?

Published on 25 Apr 2026 - 4:48

score 194 · Answer 14 · 2026-04-16 00:45:33

194

Views

Prove there is at most one subfield isomorphic to $\mathbb{F}_q$ and find intersection of two subfields

Published on 16 Apr 2026 - 0:45

score 379 · Answer 15 · 2026-04-16 09:21:09

379

Views

Which of the following quotient rings is not a field?

Published on 16 Apr 2026 - 9:21

List Question

What is the meaning of the notation $x\in K, x^{\rho\circ\sigma}$ where $\rho\in \operatorname{Aut}(K),\sigma:K\to\mathbb C$

A finite ring of matrices is a finite field

Vector space basis theorem, can it be generalized to R-modules?

$\mathbb Q(\sqrt{2},i)=\mathbb Q(\sqrt{-2},i)$

$Norm_{(\mathbb Q(\zeta_p)|\mathbb Q)}(1-\zeta_p)=p$

$K=F(\alpha)$ if $K$ is a quadratic extension

Corollary 15.3.8 from Artin (degrees of field extensions)

Showing that if $F,G \in k[x_1, ..., x_n]$ are two polynomials such that $V(F,G)$ is irreducible, that dim$(V(F,G))$ does not have to be $n - 2$

How to show that if p is prime and m,n are natural numbers then $p^m -1 | p^n -1$

Weird Invariant of Finite Reflection Groups

How to know under multiplication modulo operation the set is closed or not

Proving $\mathbb{Q}(r)$ is Galois over $\mathbb{Q}$ ?

Is the intersection of two subgroups, defined below, always trivial?

Prove there is at most one subfield isomorphic to $\mathbb{F}_q$ and find intersection of two subfields

Which of the following quotient rings is not a field?

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