List questions from euclidean-domain

Published on 22 Mar 2026 - 0:09

91

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Comparing orders induced by euclidean function and divisibility in euclidean domain

Published on 22 Mar 2026 - 3:36

2.9k

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$\mathbb{Z}[i] / (2+3i)$ has 13 elements

Published on 17 Mar 2026 - 16:19

976

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Dividing one polynomial by another

Published on 20 Mar 2026 - 7:29

64

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If the norm of $\alpha \in \mathbb{Z}[i]$ is a square, show that $\alpha$ is a square in $\mathbb{Z}[i]$

Published on 22 Mar 2026 - 5:41

691

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Are 2x2 matrices on a Euclidean domain a Euclidean domain?

Published on 22 Mar 2026 - 12:42

129

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Showing that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$.

Published on 20 Mar 2026 - 4:07

196

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Maximizing the Euclidean Distance of a Constrained Sum

Published on 19 Mar 2026 - 22:18

505

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Norm-Euclidean fields

Published on 20 Mar 2026 - 0:21

320

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Showing $(3 + \sqrt{3})$ is not a prime ideal in $\mathbb{Z}[\sqrt{3}]$

Published on 19 Mar 2026 - 18:29

3k

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Definition of a Euclidean domain

Published on 20 Mar 2026 - 4:01

176

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Why are irreducible elements prime in Euclidean domain?

Published on 22 Mar 2026 - 20:55

416

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"Let $R$ be an integral domain. Assuming that the Division Algorithm holds in $R[x]$, prove that $R$ is a field."

Published on 22 Mar 2026 - 23:04

303

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Question about proof in Neukirch's Algebraic Number Theory

Published on 23 Mar 2026 - 13:19

116

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Is $\mathbb{R}[x^2,x^3]=\{f=\sum_{i=0}^n a_ix^i\in\mathbb{R}[x]:a_1=0\}$ is Euclidean Domain?

Published on 23 Mar 2026 - 2:59

List Question

Ring of remainders definition

Comparing orders induced by euclidean function and divisibility in euclidean domain

$\mathbb{Z}[i] / (2+3i)$ has 13 elements

Dividing one polynomial by another

If the norm of $\alpha \in \mathbb{Z}[i]$ is a square, show that $\alpha$ is a square in $\mathbb{Z}[i]$

Are 2x2 matrices on a Euclidean domain a Euclidean domain?

Showing that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$.

Maximizing the Euclidean Distance of a Constrained Sum

Norm-Euclidean fields

Showing $(3 + \sqrt{3})$ is not a prime ideal in $\mathbb{Z}[\sqrt{3}]$

Definition of a Euclidean domain

Why are irreducible elements prime in Euclidean domain?

"Let $R$ be an integral domain. Assuming that the Division Algorithm holds in $R[x]$, prove that $R$ is a field."

Question about proof in Neukirch's Algebraic Number Theory

Is $\mathbb{R}[x^2,x^3]=\{f=\sum_{i=0}^n a_ix^i\in\mathbb{R}[x]:a_1=0\}$ is Euclidean Domain?

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