Question

If $K:=\mathbb Q\left(\sqrt{-3}\right)$ and $R$ is the ring of integers of $K$, then $R^{\times}=\mathbb Z\big/6\mathbb Z$

score 142 · Answer 1 · 2015-04-11 17:50:53

142

Views

If $K:=\mathbb Q\left(\sqrt{-3}\right)$ and $R$ is the ring of integers of $K$, then $R^{\times}=\mathbb Z\big/6\mathbb Z$

Published on 11 Apr 2015 - 17:50

score 832 · Answer 2 · 2015-04-12 21:12:10

832

Views

Show that the ring of integers $A$ of the cubic field $\mathbb Q[x]$ with $x^3=2$ is principal.

Published on 12 Apr 2015 - 21:12

score 172 · Answer 3 · 2015-05-30 17:42:59

172

Views

Who first used the notation $\mathcal{O}_K$ for ring of integers?

Published on 30 May 2015 - 17:42

score 622 · Answer 4 · 2015-09-18 00:53:44

622

Views

Prove that a specific ring of integers is not monogenic

Published on 18 Sep 2015 - 0:53

score 98 · Answer 5 · 2015-10-25 14:30:01

98

Views

Conway's proof of the Euclid lemma

Published on 25 Oct 2015 - 14:30

score 1k · Answer 6 · 2015-12-02 14:52:07

1k

Views

Idea behind the definition of different ideal

Published on 02 Dec 2015 - 14:52

score 342 · Answer 7 · 2026-03-15 08:45:20

342

Views

Use of GCD when solving linear equations in a ring of integers

Published on 15 Mar 2026 - 8:45

score 974 · Answer 8 · 2026-03-19 06:27:21

974

Views

How to compute the integral closure of $\Bbb{Z}$ in $\mathbb Q(\sqrt[n]{p})$?

Published on 19 Mar 2026 - 6:27

score 923 · Answer 9 · 2015-12-26 11:47:34

923

Views

$p$ is a positive integer and $(p)$ is a maximal ideal in the ring $(\mathbb Z, +,\cdot)$, then $p$ is a prime number

Published on 26 Dec 2015 - 11:47

score 482 · Answer 10 · 2026-02-27 15:37:58

482

Views

Determining when ring of integers is $\mathbb{Z}[\theta]$

Published on 27 Feb 2026 - 15:37

score 383 · Answer 11 · 2013-05-31 01:05:05

383

Views

Ring of integers of $K=\Bbb Q[u]$ where $u=\sqrt[3]{p^2q}$

Published on 31 May 2013 - 1:05

score 1.3k · Answer 12 · 2013-08-08 15:13:46

1.3k

Views

The ring of integers of the composite of two fields

Published on 08 Aug 2013 - 15:13

score 608 · Answer 13 · 2013-08-25 07:33:52

608

Views

Ring of integers in a cubic extension

Published on 25 Aug 2013 - 7:33

score 725 · Answer 14 · 2017-05-19 00:04:38

725

Views

Existence of a fundamental solution to the Pell's equation

Published on 19 May 2017 - 0:04

score 91 · Answer 15 · 2017-05-26 16:15:36

91

Views

Why $\mathbb{Z}[\theta]\,/\,\mathcal{P} \simeq \mathbb{F}_{p^e}$ for any non-zero prime ideal $\mathcal{P}$ of $\mathbb{Z}[\theta]$?

Published on 26 May 2017 - 16:15

List Question

If $K:=\mathbb Q\left(\sqrt{-3}\right)$ and $R$ is the ring of integers of $K$, then $R^{\times}=\mathbb Z\big/6\mathbb Z$

Show that the ring of integers $A$ of the cubic field $\mathbb Q[x]$ with $x^3=2$ is principal.

Who first used the notation $\mathcal{O}_K$ for ring of integers?

Prove that a specific ring of integers is not monogenic

Conway's proof of the Euclid lemma

Idea behind the definition of different ideal

Use of GCD when solving linear equations in a ring of integers

How to compute the integral closure of $\Bbb{Z}$ in $\mathbb Q(\sqrt[n]{p})$?

$p$ is a positive integer and $(p)$ is a maximal ideal in the ring $(\mathbb Z, +,\cdot)$, then $p$ is a prime number

Determining when ring of integers is $\mathbb{Z}[\theta]$

Ring of integers of $K=\Bbb Q[u]$ where $u=\sqrt[3]{p^2q}$

The ring of integers of the composite of two fields

Ring of integers in a cubic extension

Existence of a fundamental solution to the Pell's equation

Why $\mathbb{Z}[\theta]\,/\,\mathcal{P} \simeq \mathbb{F}_{p^e}$ for any non-zero prime ideal $\mathcal{P}$ of $\mathbb{Z}[\theta]$?

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