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 143 · Answer 1 · 2026-03-25 07:45:48

143

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 25 Mar 2026 - 7:45

score 833 · Answer 2 · 2026-03-25 07:45:50

833

Views

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

Published on 25 Mar 2026 - 7:45

score 173 · Answer 3 · 2026-03-25 11:06:26

173

Views

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

Published on 25 Mar 2026 - 11:06

score 623 · Answer 4 · 2026-03-25 07:47:58

623

Views

Prove that a specific ring of integers is not monogenic

Published on 25 Mar 2026 - 7:47

score 101 · Answer 5 · 2026-04-09 16:00:21

101

Views

Conway's proof of the Euclid lemma

Published on 09 Apr 2026 - 16:00

score 1k · Answer 6 · 2026-04-14 03:08:52

1k

Views

Idea behind the definition of different ideal

Published on 14 Apr 2026 - 3:08

score 344 · Answer 7 · 2026-04-26 08:10:49

344

Views

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

Published on 26 Apr 2026 - 8:10

score 975 · Answer 8 · 2026-04-18 12:33:43

975

Views

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

Published on 18 Apr 2026 - 12:33

score 925 · Answer 9 · 2026-04-03 23:06:00

925

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 03 Apr 2026 - 23:06

score 484 · Answer 10 · 2026-05-01 07:17:06

484

Views

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

Published on 01 May 2026 - 7:17

score 384 · Answer 11 · 2026-03-25 07:44:54

384

Views

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

Published on 25 Mar 2026 - 7:44

score 1.3k · Answer 12 · 2026-03-25 11:06:56

1.3k

Views

The ring of integers of the composite of two fields

Published on 25 Mar 2026 - 11:06

score 610 · Answer 13 · 2026-03-27 11:18:40

610

Views

Ring of integers in a cubic extension

Published on 27 Mar 2026 - 11:18

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 93 · Answer 15 · 2026-04-08 15:08:55

93

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 08 Apr 2026 - 15:08

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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