List questions from euclidean-domain

Published on 12 Dec 2017 - 22:02

32

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$R$ euclidean domain, show $\tilde{N}(a)=\min_{0\neq x\in\left<a\right>}N(x)$ is a norm

Published on 13 Dec 2017 - 3:15

467

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Looking for more direct proof of non-existence of "Euclidean algorithm norm" for $\mathbb{Z}[\sqrt{-5}]$

Published on 03 Jan 2018 - 13:40

7.5k

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The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain

Published on 26 Feb 2011 - 12:58

246

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Natural Euclidean Function Not Satisfying the $d$-inequality

Published on 14 Oct 2011 - 7:25

2.6k

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A question about Euclidean Domain

Published on 15 Jun 2012 - 16:43

109

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Problem in ordering of the $\mathbb{C}$

Published on 09 Aug 2020 - 17:26

145

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About a subset of $\mathbb Q[x]$ of polynomials $f$ such that $f(n)=f(-n)$ for every $n$ in $\mathbb N$

Published on 05 Sep 2020 - 16:54

134

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Algorithmic Euclidean domains.

Published on 05 Sep 2020 - 18:48

106

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Extending Euclidean Valuation (algebra chapter 0)

Published on 27 Sep 2020 - 16:14

115

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Does every pair of non-zero elements of $Z[\sqrt{3}]$ has a gcd?

Published on 19 Oct 2020 - 14:43

57

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How many solutions there are for $x \in Z_6$ in the following equations?

Published on 19 Oct 2020 - 21:24

30

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How do I find $\displaystyle {\inf\limits_{n,m} \dfrac {\deg (m)} {\deg (r)}}\ ?$

Published on 26 Mar 2026 - 11:17

824

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Show that the ring of formal power series is a Euclidean domain.

Published on 17 Nov 2020 - 10:36

132

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Euclidean division in quotients of polynomial rings

Published on 27 Nov 2020 - 22:22

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Can you give me some recommendations to understand this proof?

$R$ euclidean domain, show $\tilde{N}(a)=\min_{0\neq x\in\left<a\right>}N(x)$ is a norm

Looking for more direct proof of non-existence of "Euclidean algorithm norm" for $\mathbb{Z}[\sqrt{-5}]$

The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain

Natural Euclidean Function Not Satisfying the $d$-inequality

A question about Euclidean Domain

Problem in ordering of the $\mathbb{C}$

About a subset of $\mathbb Q[x]$ of polynomials $f$ such that $f(n)=f(-n)$ for every $n$ in $\mathbb N$

Algorithmic Euclidean domains.

Extending Euclidean Valuation (algebra chapter 0)

Does every pair of non-zero elements of $Z[\sqrt{3}]$ has a gcd?

How many solutions there are for $x \in Z_6$ in the following equations?

How do I find $\displaystyle {\inf\limits_{n,m} \dfrac {\deg (m)} {\deg (r)}}\ ?$

Show that the ring of formal power series is a Euclidean domain.

Euclidean division in quotients of polynomial rings

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