List questions from euclidean-domain

Published on 11 Jan 2021 - 17:39

91

Views

Find a generator of the ideal generated by $3$ and $2-2\sqrt{-2}$ in ${\mathbb{Z}\left[\sqrt{-2}\right]}$

Published on 16 Jan 2021 - 10:57

206

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Properties of size function in a general Euclidean domain

Published on 02 Feb 2021 - 19:09

364

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An application of Brouwer fixed point Theorem

Published on 07 Feb 2021 - 14:59

93

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Proving that $aR + bR = \gcd(a, b)R.$

Published on 16 Feb 2021 - 4:09

351

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On $C^1$ convex domain

Published on 01 Mar 2021 - 19:36

152

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Regarding the Tensor Product of Quotient Rings of a Euclidean Domain

Published on 13 Mar 2021 - 5:49

355

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Show that $\mathbb{Z}[\sqrt{14}]$ is not an Euclidean domain with regard to this norm.

Published on 14 Mar 2021 - 18:30

194

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

Published on 16 Mar 2021 - 17:23

205

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When is $R[x]$ a Euclidean domain?

Published on 30 Mar 2021 - 3:53

48

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Euclidean functions on polynomial rings over fields

Published on 10 Apr 2021 - 6:55

491

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

Published on 23 Feb 2026 - 4:01

289

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Angle between arbitrary rectangle and horizontal plane

Published on 12 Apr 2021 - 7:12

120

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Compactness and Cantor's Criterion

Published on 14 Apr 2021 - 21:40

55

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Of those domains that were proven to be Euclidean but are not norm-Euclidean, can we really perform Euclidean algorithm in them?

Published on 13 May 2021 - 19:37

List Question

Is $\mathbb{Z}[i,\varphi]$ a Euclidean domain?

Find a generator of the ideal generated by $3$ and $2-2\sqrt{-2}$ in ${\mathbb{Z}\left[\sqrt{-2}\right]}$

Properties of size function in a general Euclidean domain

An application of Brouwer fixed point Theorem

Proving that $aR + bR = \gcd(a, b)R.$

On $C^1$ convex domain

Regarding the Tensor Product of Quotient Rings of a Euclidean Domain

Show that $\mathbb{Z}[\sqrt{14}]$ is not an Euclidean domain with regard to this norm.

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

When is $R[x]$ a Euclidean domain?

Euclidean functions on polynomial rings over fields

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

Angle between arbitrary rectangle and horizontal plane

Compactness and Cantor's Criterion

Of those domains that were proven to be Euclidean but are not norm-Euclidean, can we really perform Euclidean algorithm in them?

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