Question

How can I prove these polynomials are minimal?

score 51 · Answer 1 · 2026-04-12 01:18:34

51

Views

How can I prove these polynomials are minimal?

Published on 12 Apr 2026 - 1:18

score 239 · Answer 2 · 2026-04-11 15:00:48

239

Views

Simple extension is splitting field of $f=X^p-X+a \in K[X]$ with $char(K)=p$

Published on 11 Apr 2026 - 15:00

score 73 · Answer 3 · 2026-04-15 18:07:08

73

Views

Irreducible polynomial over $\mathbb{Q}(\sqrt[3]{2})$

Published on 15 Apr 2026 - 18:07

score 671 · Answer 4 · 2026-04-17 04:15:13

671

Views

Let $\bar{\mathbb{Q}}$ be the algebraic closure of $\mathbb{Q}$. What is the cardinality of a transcendental extension $K\setminus \bar{\mathbb{Q}}$?

Published on 17 Apr 2026 - 4:15

score 147 · Answer 5 · 2026-04-16 11:32:23

147

Views

Show that $L/L_s$ is purely inseparable and $L_s/ K$ is separable.

Published on 16 Apr 2026 - 11:32

score 257 · Answer 6 · 2026-04-15 11:56:17

257

Views

Question regarding $\mathbb R$-automorphisms of the extension $\mathbb C:\mathbb R$

Published on 15 Apr 2026 - 11:56

score 341 · Answer 7 · 2026-04-14 11:43:36

341

Views

How to write Euler product and Zeta function for $K = \mathbb{Q}(\sqrt{3})$

Published on 14 Apr 2026 - 11:43

score 684 · Answer 8 · 2026-04-17 01:17:18

684

Views

Degree of field extension of $ [\mathbb Q( 2^{1/2} + 2^{1/3} +2^{1/4}+2^{1/5}+\cdots 2^{1/n}) : \mathbb Q(2^{1/2}) ]$

Published on 17 Apr 2026 - 1:17

score 1k · Answer 9 · 2026-04-15 16:32:35

1k

Views

"Two algebraically closed fields with char $0$ and same cardinality $\kappa> \aleph_0$ are isomorphic." Any reference for this result?

Published on 15 Apr 2026 - 16:32

score 702 · Answer 10 · 2026-04-16 06:28:13

702

Views

Create an explicit extension of the 2-adic metric to $\mathbb{R}$ in which at least $(1,\infty)$ is connected.

Published on 16 Apr 2026 - 6:28

score 78 · Answer 11 · 2026-04-25 03:40:19

78

Views

Depth-free Frobenius map computation in $\mathbb{F}_{p^l}$

Published on 25 Apr 2026 - 3:40

score 164 · Answer 12 · 2026-04-14 16:27:11

164

Views

Degree of a field extension $K/\mathbb{Q}$

Published on 14 Apr 2026 - 16:27

score 344 · Answer 13 · 2026-04-14 10:21:02

344

Views

Degree of field extensions in $\mathbb{Q}$ with two algebraic elements

Published on 14 Apr 2026 - 10:21

score 4.5k · Answer 14 · 2026-04-12 05:05:12

4.5k

Views

The relationship between normal extension and the splitting field of polynomial

Published on 12 Apr 2026 - 5:05

score 697 · Answer 15 · 2026-04-15 06:05:14

697

Views

Norm of an ideal with two generators in a ring of integers

Published on 15 Apr 2026 - 6:05

List Question

How can I prove these polynomials are minimal?

Simple extension is splitting field of $f=X^p-X+a \in K[X]$ with $char(K)=p$

Irreducible polynomial over $\mathbb{Q}(\sqrt[3]{2})$

Let $\bar{\mathbb{Q}}$ be the algebraic closure of $\mathbb{Q}$. What is the cardinality of a transcendental extension $K\setminus \bar{\mathbb{Q}}$?

Show that $L/L_s$ is purely inseparable and $L_s/ K$ is separable.

Question regarding $\mathbb R$-automorphisms of the extension $\mathbb C:\mathbb R$

How to write Euler product and Zeta function for $K = \mathbb{Q}(\sqrt{3})$

Degree of field extension of $ [\mathbb Q( 2^{1/2} + 2^{1/3} +2^{1/4}+2^{1/5}+\cdots 2^{1/n}) : \mathbb Q(2^{1/2}) ]$

"Two algebraically closed fields with char $0$ and same cardinality $\kappa> \aleph_0$ are isomorphic." Any reference for this result?

Create an explicit extension of the 2-adic metric to $\mathbb{R}$ in which at least $(1,\infty)$ is connected.

Depth-free Frobenius map computation in $\mathbb{F}_{p^l}$

Degree of a field extension $K/\mathbb{Q}$

Degree of field extensions in $\mathbb{Q}$ with two algebraic elements

The relationship between normal extension and the splitting field of polynomial

Norm of an ideal with two generators in a ring of integers

Trending Questions

Popular # Hahtags

Popular Questions