Question

How to show that the class number is bounded by Minkowski's bound?

score 174 · Answer 1 · 2018-07-31 09:32:08

174

Views

How to show that the class number is bounded by Minkowski's bound?

Published on 31 Jul 2018 - 9:32

score 205 · Answer 2 · 2018-07-31 12:20:14

205

Views

How do I know that $q(\alpha)\neq 0$ in this proof? And one more question.

Published on 31 Jul 2018 - 12:20

score 277 · Answer 3 · 2026-03-28 22:26:28

277

Views

Field Extensions: Impossibility of trisecting an angle with compass and straightedge. Constructing arbitrary points?

Published on 28 Mar 2026 - 22:26

score 770 · Answer 4 · 2018-07-31 19:37:13

770

Views

$\mathbb{Q}(\sqrt d)$ is the smallest subfield of $\mathbb{C}$ containing $\mathbb{Q}$ and $\sqrt d$ using field norm

Published on 31 Jul 2018 - 19:37

score 50 · Answer 5 · 2026-03-30 03:55:16

50

Views

Algebraic Structures that are similar to Vector Spaces but exist over a Commutative Ring as opposed to a Field?

Published on 30 Mar 2026 - 3:55

score 44 · Answer 6 · 2018-08-01 06:14:34

44

Views

Is $\mathbb{R}^2$ with product defined like $(x, y)\cdot(a, b)=(ax, by)$, and usual addition, a field?

Published on 01 Aug 2018 - 6:14

score 692 · Answer 7 · 2026-03-26 08:02:24

692

Views

On the proof of existence of algebraic closure using Zorn's Lemma in Patrick Morandi's Field and Galois Theory

Published on 26 Mar 2026 - 8:02

score 163 · Answer 8 · 2026-03-26 20:39:40

163

Views

What exactly is a linearized polynomial in field theory?

Published on 26 Mar 2026 - 20:39

score 37 · Answer 9 · 2018-08-01 12:12:20

37

Views

field are domains.

Published on 01 Aug 2018 - 12:12

score 83 · Answer 10 · 2026-03-29 06:33:44

83

Views

What is the general form of the valid polynomial equations over $\mathbb Q$ relating $\alpha,\beta,\gamma$ and $\delta$?

Published on 29 Mar 2026 - 6:33

score 879 · Answer 11 · 2018-08-03 06:35:06

879

Views

Is it true that $F(\alpha)\cong F[x]/(p(x))$?

Published on 03 Aug 2018 - 6:35

score 76 · Answer 12 · 2026-03-26 07:59:05

76

Views

For a field $F$, what are the elements of $U(F[x])$?

Published on 26 Mar 2026 - 7:59

score 579 · Answer 13 · 2026-02-23 01:22:13

579

Views

A perfect field that is neither of characteristic $0$ nor algebraically closed

Published on 23 Feb 2026 - 1:22

score 321 · Answer 14 · 2026-03-29 04:47:22

321

Views

Automorphisms of Finite Field Extension

Published on 29 Mar 2026 - 4:47

score 439 · Answer 15 · 2026-03-26 22:16:06

439

Views

Degree of finite field extension by adjoining root of minimal polynomial

Published on 26 Mar 2026 - 22:16

List Question

How to show that the class number is bounded by Minkowski's bound?

How do I know that $q(\alpha)\neq 0$ in this proof? And one more question.

Field Extensions: Impossibility of trisecting an angle with compass and straightedge. Constructing arbitrary points?

$\mathbb{Q}(\sqrt d)$ is the smallest subfield of $\mathbb{C}$ containing $\mathbb{Q}$ and $\sqrt d$ using field norm

Algebraic Structures that are similar to Vector Spaces but exist over a Commutative Ring as opposed to a Field?

Is $\mathbb{R}^2$ with product defined like $(x, y)\cdot(a, b)=(ax, by)$, and usual addition, a field?

On the proof of existence of algebraic closure using Zorn's Lemma in Patrick Morandi's Field and Galois Theory

What exactly is a linearized polynomial in field theory?

field are domains.

What is the general form of the valid polynomial equations over $\mathbb Q$ relating $\alpha,\beta,\gamma$ and $\delta$?

Is it true that $F(\alpha)\cong F[x]/(p(x))$?

For a field $F$, what are the elements of $U(F[x])$?

A perfect field that is neither of characteristic $0$ nor algebraically closed

Automorphisms of Finite Field Extension

Degree of finite field extension by adjoining root of minimal polynomial

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