Question

Unable to understand the relation between Field Extensions, Polynomial Quotient Rings generated by Ideals, & Polynomial Roots

score 185 · Answer 1 · 2026-04-14 06:35:06

185

Views

Unable to understand the relation between Field Extensions, Polynomial Quotient Rings generated by Ideals, & Polynomial Roots

Published on 14 Apr 2026 - 6:35

score 78 · Answer 2 · 2026-04-17 02:01:21

78

Views

Is $\mathbb{Q}(\sqrt[3]3)$ = $\{a+b\sqrt[3]3+c\sqrt[3]9 | a,b,c \in \mathbb{Q}\}$ a field?

Published on 17 Apr 2026 - 2:01

score 48 · Answer 3 · 2026-04-13 23:04:17

48

Views

A dimension problem related to an abelian extension of a field

Published on 13 Apr 2026 - 23:04

score 57 · Answer 4 · 2026-04-15 12:51:58

57

Views

Element in $\mathbb{Q}(\sqrt[3]{5})$ satisfying quadratic equation

Published on 15 Apr 2026 - 12:51

score 97 · Answer 5 · 2026-04-14 03:05:25

97

Views

$K(u, v) = K(u+v)$ when characteristic of $K=0$?

Published on 14 Apr 2026 - 3:05

score 91 · Answer 6 · 2026-04-15 04:38:10

91

Views

Is $\mathbb{Q}(\sqrt[3]{3},\sqrt{3},i)$ a splitting field over $\mathbb{Q}?$

Published on 15 Apr 2026 - 4:38

score 366 · Answer 7 · 2026-04-15 07:44:07

366

Views

Irreducible polynomial in integers modulo p

Published on 15 Apr 2026 - 7:44

score 90 · Answer 8 · 2026-04-16 14:16:49

90

Views

Possible $|F(\alpha, \beta):F|$ where $|F(\alpha):F|=6$ and $|F(\beta):F|=15$?

Published on 16 Apr 2026 - 14:16

score 119 · Answer 9 · 2026-04-15 06:04:42

119

Views

$\operatorname{dim}_{\mathbb C} \mathbb C \otimes_{\mathbb R} \mathbb C$ vs. $\operatorname{dim}_{\mathbb R} \mathbb C \otimes_{\mathbb R} \mathbb C$

Published on 15 Apr 2026 - 6:04

score 127 · Answer 10 · 2026-04-16 15:17:29

127

Views

What is the practical use of constructing an extension $\mathbb R[x]/\langle p(x) \rangle$ to find a root rather going to $\mathbb C$?

Published on 16 Apr 2026 - 15:17

score 142 · Answer 11 · 2026-04-14 05:15:13

142

Views

Proof of If $K$ is a finite extension of $F$, then $K$ is algebraic and finitely generated over $F$

Published on 14 Apr 2026 - 5:15

score 38 · Answer 12 · 2026-04-13 21:24:39

38

Views

Inequality involving degrees of field extensions

Published on 13 Apr 2026 - 21:24

score 186 · Answer 13 · 2026-04-14 16:28:03

186

Views

L is normal extension if it's splitting field

Published on 14 Apr 2026 - 16:28

score 168 · Answer 14 · 2026-04-15 19:13:23

168

Views

Question on the irreducibility of $x^4 - 10x^2 +1$

Published on 15 Apr 2026 - 19:13

score 57 · Answer 15 · 2026-04-17 13:52:23

57

Views

Find a particular intermediate field $M$ such that $\mathbb{Q}\subset M\subset\mathbb{Q}(\sqrt{\frac{3+i\sqrt{7}}{2}})$.

Published on 17 Apr 2026 - 13:52

List Question

Unable to understand the relation between Field Extensions, Polynomial Quotient Rings generated by Ideals, & Polynomial Roots

Is $\mathbb{Q}(\sqrt[3]3)$ = $\{a+b\sqrt[3]3+c\sqrt[3]9 | a,b,c \in \mathbb{Q}\}$ a field?

A dimension problem related to an abelian extension of a field

Element in $\mathbb{Q}(\sqrt[3]{5})$ satisfying quadratic equation

$K(u, v) = K(u+v)$ when characteristic of $K=0$?

Is $\mathbb{Q}(\sqrt[3]{3},\sqrt{3},i)$ a splitting field over $\mathbb{Q}?$

Irreducible polynomial in integers modulo p

Possible $|F(\alpha, \beta):F|$ where $|F(\alpha):F|=6$ and $|F(\beta):F|=15$?

$\operatorname{dim}_{\mathbb C} \mathbb C \otimes_{\mathbb R} \mathbb C$ vs. $\operatorname{dim}_{\mathbb R} \mathbb C \otimes_{\mathbb R} \mathbb C$

What is the practical use of constructing an extension $\mathbb R[x]/\langle p(x) \rangle$ to find a root rather going to $\mathbb C$?

Proof of If $K$ is a finite extension of $F$, then $K$ is algebraic and finitely generated over $F$

Inequality involving degrees of field extensions

L is normal extension if it's splitting field

Question on the irreducibility of $x^4 - 10x^2 +1$

Find a particular intermediate field $M$ such that $\mathbb{Q}\subset M\subset\mathbb{Q}(\sqrt{\frac{3+i\sqrt{7}}{2}})$.

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