List questions from euclidean-domain

Published on 15 Apr 2026 - 17:21

808

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Find the equation of the two tangent planes to the sphere $x^2+y^2+z^2-2y-6z+5=0$ which are parallel to the plane $2x+2y-z=0$

Published on 16 Apr 2026 - 13:09

719

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When is $\mathbb Z[\sqrt d]$ a Euclidean or principal ideal domain?

Published on 13 Apr 2026 - 10:52

56

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Prove that $\mathcal{O}_K$ for $K = \mathbb{Q}(\sqrt{3})$ is euclidean

Published on 15 Apr 2026 - 23:31

174

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Smallest residue over $\Bbb Z[\omega]$

Published on 10 May 2026 - 13:49

97

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Euclidean mapping question

Published on 10 Apr 2026 - 3:17

129

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For this broad definition of Euclidean domain, is there a non-trivial example with finite set of norms?

Published on 26 Mar 2026 - 8:02

81

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A particular euclidean function implies the domain is local?

Published on 14 Apr 2026 - 2:11

268

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Properties of division with remainder

Published on 10 Apr 2026 - 3:40

355

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Show that $\delta$ is a Euclidean valuation on the Gaussian Integers

Published on 15 Apr 2026 - 23:57

47

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Let $p_1,...,p_s$ be a maximal system of irreducible divisors, pairwise non-associated, of $ab$ in a euclidean domain.

Published on 11 Apr 2026 - 13:16

130

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The structure theorem in the context of finite abelian groups.

Published on 10 Apr 2026 - 5:51

554

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Part of proving R[x] is not a Euclidean domain given R is not a field

Published on 15 Apr 2026 - 8:17

278

Views

Associated elements on Euclidean Domains

Published on 14 Apr 2026 - 19:09

125

Views

Showing elements in a Euclidean domain are coprime

Published on 15 Apr 2026 - 14:49

List Question

Proving Gaussian Integers as an Euclidean Domain

Find the equation of the two tangent planes to the sphere $x^2+y^2+z^2-2y-6z+5=0$ which are parallel to the plane $2x+2y-z=0$

When is $\mathbb Z[\sqrt d]$ a Euclidean or principal ideal domain?

Prove that $\mathcal{O}_K$ for $K = \mathbb{Q}(\sqrt{3})$ is euclidean

Smallest residue over $\Bbb Z[\omega]$

Euclidean mapping question

For this broad definition of Euclidean domain, is there a non-trivial example with finite set of norms?

A particular euclidean function implies the domain is local?

Properties of division with remainder

Show that $\delta$ is a Euclidean valuation on the Gaussian Integers

Let $p_1,...,p_s$ be a maximal system of irreducible divisors, pairwise non-associated, of $ab$ in a euclidean domain.

The structure theorem in the context of finite abelian groups.

Part of proving R[x] is not a Euclidean domain given R is not a field

Associated elements on Euclidean Domains

Showing elements in a Euclidean domain are coprime

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