Question

Linear transformations over PIDs/ EDs

score 36 · Answer 1 · 2022-01-21 17:41:42

36

Views

Linear transformations over PIDs/ EDs

Published on 21 Jan 2022 - 17:41

score 280 · Answer 2 · 2022-01-25 00:39:04

280

Views

Why does this proof generalize for all norms? $\mathbb Z[\sqrt{-5}]$ is not an Euclidean Domain.

Published on 25 Jan 2022 - 0:39

score 420 · Answer 3 · 2026-03-26 22:52:33

420

Views

Surjective ring homomorphism from $\mathbb{Z}[i] \to \mathbb{Z}_q$

Published on 26 Mar 2026 - 22:52

score 37 · Answer 4 · 2022-05-17 01:54:54

37

Views

Does a euclidian size function distribute over addition?

Published on 17 May 2022 - 1:54

score 205 · Answer 5 · 2022-05-28 12:52:54

205

Views

Prove Bézout's lemma for $\mathbb{Z}[(1+\sqrt{-19})/2]$

Published on 28 May 2022 - 12:52

score 55 · Answer 6 · 2022-06-07 11:05:31

55

Views

A Textbook Problem, Slightly Modified

Published on 07 Jun 2022 - 11:05

score 143 · Answer 7 · 2022-06-08 14:59:18

143

Views

$F$ be a Euclidean domain satisfying $\delta(a + b) ≤ \max(\delta(a),\delta(b))$ then $F$ is a field $K$ or $F \subset K[x]$

Published on 08 Jun 2022 - 14:59

score 105 · Answer 8 · 2022-06-08 19:48:31

Show that $\mathbb{Z}[\sqrt{n}]$ is a Euclidean domain for $n = −1,−2, 2, 3$, where $\mathbb{Z}[\sqrt{n}] =\{a + b\sqrt{n} :a,b \in \mathbb{Z}\}$

score 49 · Answer 9 · 2022-06-08 20:07:11

49

Views

Let $D = \mathbb{Z}[i\sqrt{3}]$ and $v(a +bi\sqrt{3}) = a^2 + 3b^2$ then show that $v$ is not Euclidean evaluation map on $D$

Published on 08 Jun 2022 - 20:07

score 35 · Answer 10 · 2022-07-11 00:56:41

35

Views

Are there any Euclidean Rings with a norm which is not additive nor multiplicative?

Published on 11 Jul 2022 - 0:56

score 151 · Answer 11 · 2022-10-14 04:47:16

151

Views

$W^{k,p}_{0}$ is scale invariant

Published on 14 Oct 2022 - 4:47

score 293 · Answer 12 · 2026-02-23 05:40:54

293

Views

How to show the quadratic integer ring O is not a UFD.

Published on 23 Feb 2026 - 5:40

score 98 · Answer 13 · 2022-11-02 12:26:12

98

Views

Doubts about the form of the Euclidean projection

Published on 02 Nov 2022 - 12:26

score 94 · Answer 14 · 2022-11-18 18:45:13

94

Views

Diophantine equation $a^{2} = b^{4} + b^{3} + b^{2} + b + 1$

Published on 18 Nov 2022 - 18:45

score 68 · Answer 15 · 2022-11-20 09:48:14

68

Views

Explicit expression of closest integers in the proof that $\mathbb{Z} \left[ \sqrt {2} \right]$ is euclidean.

Published on 20 Nov 2022 - 9:48

List Question

Linear transformations over PIDs/ EDs

Why does this proof generalize for all norms? $\mathbb Z[\sqrt{-5}]$ is not an Euclidean Domain.

Surjective ring homomorphism from $\mathbb{Z}[i] \to \mathbb{Z}_q$

Does a euclidian size function distribute over addition?

Prove Bézout's lemma for $\mathbb{Z}[(1+\sqrt{-19})/2]$

A Textbook Problem, Slightly Modified

$F$ be a Euclidean domain satisfying $\delta(a + b) ≤ \max(\delta(a),\delta(b))$ then $F$ is a field $K$ or $F \subset K[x]$

Show that $\mathbb{Z}[\sqrt{n}]$ is a Euclidean domain for $n = −1,−2, 2, 3$, where $\mathbb{Z}[\sqrt{n}] =\{a + b\sqrt{n} :a,b \in \mathbb{Z}\}$

Let $D = \mathbb{Z}[i\sqrt{3}]$ and $v(a +bi\sqrt{3}) = a^2 + 3b^2$ then show that $v$ is not Euclidean evaluation map on $D$

Are there any Euclidean Rings with a norm which is not additive nor multiplicative?

$W^{k,p}_{0}$ is scale invariant

How to show the quadratic integer ring O is not a UFD.

Doubts about the form of the Euclidean projection

Diophantine equation $a^{2} = b^{4} + b^{3} + b^{2} + b + 1$

Explicit expression of closest integers in the proof that $\mathbb{Z} \left[ \sqrt {2} \right]$ is euclidean.

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