Question

How to prove that this multivariable polynomial quotientring is a field, and to what field is it isomorphic?

score 64 · Answer 1 · 2026-04-14 12:49:06

64

Views

How to prove that this multivariable polynomial quotientring is a field, and to what field is it isomorphic?

Published on 14 Apr 2026 - 12:49

score 129 · Answer 2 · 2026-04-15 23:16:49

129

Views

A commutative diagram for $F(\alpha) \cong F[x] / \langle p(x) \rangle$

Published on 15 Apr 2026 - 23:16

score 123 · Answer 3 · 2026-05-11 10:09:57

123

Views

Algebraic integers: Explicit proof that $\prod_{i,j} (x^2+\alpha_i x+\beta_j)$ (with $\alpha_i$ and $\beta_j$ conjugates) has integer coefficients.

Published on 11 May 2026 - 10:09

score 154 · Answer 4 · 2026-04-16 06:08:00

154

Views

The contraction of a symmetric tensor $S_{\mu\nu}$ with another tensor $A^{\mu\nu}$ is $0$, prove that $A^{\mu\nu}$ is antisymmetric

Published on 16 Apr 2026 - 6:08

score 76 · Answer 5 · 2026-04-10 08:56:06

76

Views

Characterzation of the complex numbers

Published on 10 Apr 2026 - 8:56

score 55 · Answer 6 · 2026-04-14 06:44:38

55

Views

Characterizing all primitive elements of a simple extension

Published on 14 Apr 2026 - 6:44

score 149 · Answer 7 · 2026-04-17 08:11:03

149

Views

$f(X) = X^9 - 2dX^6 + 3d^2 X^3 - d^3$ irreducible in $\mathbb{Q}[X]$ for given cube-free integer $d>1$.

Published on 17 Apr 2026 - 8:11

score 84 · Answer 8 · 2026-04-14 15:09:20

84

Views

Polynomial factorisation over quotient ring

Published on 14 Apr 2026 - 15:09

score 34 · Answer 9 · 2026-04-14 07:37:11

34

Views

Endomorphism ring of a quiver representation over an algebraically closed field.

Published on 14 Apr 2026 - 7:37

score 34 · Answer 10 · 2026-04-11 09:36:05

34

Views

$\bar{x}$ notation in Field Theory

Published on 11 Apr 2026 - 9:36

score 37 · Answer 11 · 2026-04-15 19:28:56

37

Views

How do I show that $x^\frac{q-1}{2} = -1$ if $x$ is nonsquare for a finite field $k$ with order $q$

Published on 15 Apr 2026 - 19:28

score 90 · Answer 12 · 2026-04-14 05:39:42

90

Views

Regarding the isomorphism $PGL(2,K) \cong GL(2,K)/Scal(2, K)$ and a degree of a field extension

Published on 14 Apr 2026 - 5:39

score 102 · Answer 13 · 2026-04-14 10:23:55

102

Views

Why is this proof wrong, or not preferred?

Published on 14 Apr 2026 - 10:23

score 32 · Answer 14 · 2026-04-17 03:01:50

32

Views

"Galois group" acts transitively on irreducible factors in the context of normal extensions (not necessarily separable)

Published on 17 Apr 2026 - 3:01

score 76 · Answer 15 · 2026-04-12 10:50:19

76

Views

Finite extension of finite field

Published on 12 Apr 2026 - 10:50

List Question

How to prove that this multivariable polynomial quotientring is a field, and to what field is it isomorphic?

A commutative diagram for $F(\alpha) \cong F[x] / \langle p(x) \rangle$

Algebraic integers: Explicit proof that $\prod_{i,j} (x^2+\alpha_i x+\beta_j)$ (with $\alpha_i$ and $\beta_j$ conjugates) has integer coefficients.

The contraction of a symmetric tensor $S_{\mu\nu}$ with another tensor $A^{\mu\nu}$ is $0$, prove that $A^{\mu\nu}$ is antisymmetric

Characterzation of the complex numbers

Characterizing all primitive elements of a simple extension

$f(X) = X^9 - 2dX^6 + 3d^2 X^3 - d^3$ irreducible in $\mathbb{Q}[X]$ for given cube-free integer $d>1$.

Polynomial factorisation over quotient ring

Endomorphism ring of a quiver representation over an algebraically closed field.

$\bar{x}$ notation in Field Theory

How do I show that $x^\frac{q-1}{2} = -1$ if $x$ is nonsquare for a finite field $k$ with order $q$

Regarding the isomorphism $PGL(2,K) \cong GL(2,K)/Scal(2, K)$ and a degree of a field extension

Why is this proof wrong, or not preferred?

"Galois group" acts transitively on irreducible factors in the context of normal extensions (not necessarily separable)

Finite extension of finite field

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