List questions from quadratic-integer-rings

Published on 10 Dec 2015 - 18:46

842

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How do I prove that $\mathbb{Z}[\sqrt{19}]$ is not a UFD?

Published on 27 Jun 2016 - 14:43

261

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Prove $\Bbb{Z}[\sqrt{d}] /(a + \sqrt{d}) \cong\Bbb{Z}/n\Bbb{Z}$, where $n=|a^2-d|$.

Published on 23 Jul 2013 - 21:29

171

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Quadratic Integers and Sandwich Numbers

Published on 18 May 2017 - 4:57

171

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Quotient of quadratic integer by a maximal ideal

Published on 23 Sep 2017 - 0:13

180

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Existence of integers $a$ and $b$ such that $p = a^2 +ab+b^2$ for $p = 3 $ or $p\equiv 1 \mod 3$

Published on 11 Oct 2017 - 14:14

349

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Ideals of the quadratic integer ring $\mathbb{Z}[\sqrt{-5}]$

Published on 11 Oct 2017 - 19:58

534

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Prove that the ideal $I = \left( 3, 2 + \sqrt{-5} \right)$ is a prime ideal in $\mathbb{Z}\left[ \sqrt{-5} \right]$.

Published on 12 Oct 2017 - 1:29

23

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Some reference on quadratic rings or introductory algebraic number theory.

Published on 18 Oct 2017 - 16:03

1.8k

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Infinitely many primes in the ring of integers for any quadratic field

Published on 29 Apr 2011 - 18:09

490

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Finding the units of $\mathbb{Z}\left[\frac{1+\sqrt{-19}}{2}\right]$

Published on 10 Apr 2021 - 10:02

68

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Factorizations in $\mathbb{Z}[\theta]$

Published on 10 Apr 2021 - 10:20

39

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Understanding the difference between 2 questions.

Published on 05 Nov 2021 - 18:19

39

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Conjugation map in quadratic integer rings is an automorphism

Published on 21 Nov 2021 - 15:34

36

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Description about the set of quadratic integer with prime norm.

Published on 26 Feb 2022 - 13:47

List Question

Prove a property of the order of conductor $f$ in the field $\mathbb{Q}(\sqrt{D})$

How do I prove that $\mathbb{Z}[\sqrt{19}]$ is not a UFD?

Prove $\Bbb{Z}[\sqrt{d}] /(a + \sqrt{d}) \cong\Bbb{Z}/n\Bbb{Z}$, where $n=|a^2-d|$.

Quadratic Integers and Sandwich Numbers

Quotient of quadratic integer by a maximal ideal

Existence of integers $a$ and $b$ such that $p = a^2 +ab+b^2$ for $p = 3 $ or $p\equiv 1 \mod 3$

Ideals of the quadratic integer ring $\mathbb{Z}[\sqrt{-5}]$

Prove that the ideal $I = \left( 3, 2 + \sqrt{-5} \right)$ is a prime ideal in $\mathbb{Z}\left[ \sqrt{-5} \right]$.

Some reference on quadratic rings or introductory algebraic number theory.

Infinitely many primes in the ring of integers for any quadratic field

Finding the units of $\mathbb{Z}\left[\frac{1+\sqrt{-19}}{2}\right]$

Factorizations in $\mathbb{Z}[\theta]$

Understanding the difference between 2 questions.

Conjugation map in quadratic integer rings is an automorphism

Description about the set of quadratic integer with prime norm.

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