Question

Visualizing euclidean rings

score 161 · Answer 1 · 2026-04-17 09:13:15

161

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Visualizing euclidean rings

Published on 17 Apr 2026 - 9:13

score 590 · Answer 2 · 2026-04-11 06:04:17

590

Views

How to restrict only top range of ellipse function, and what is its domain?

Published on 11 Apr 2026 - 6:04

score 91 · Answer 3 · 2026-04-14 11:06:41

91

Views

Can anyone give me an example of an Euclidean Domain $D$ whose Euclidean Valuation at a point $a$: $v(a)$ is bigger than $\min \{v(ax) : x\in D\}$?

Published on 14 Apr 2026 - 11:06

score 30 · Answer 4 · 2026-04-15 23:34:16

30

Views

Can anyone gives me an example of $V$ such that there exists at least one pair of elements $ a,c(\neq 0 ,1) \in D$ such that $V(a) > V(ac)$

Published on 15 Apr 2026 - 23:34

score 221 · Answer 5 · 2026-04-09 11:23:27

221

Views

It is given that $a_1=\gcd(a_{11}, a_{12} , \cdots , a_{mn})$. Then prove that after elementary row and column operation we get ...

Published on 09 Apr 2026 - 11:23

score 179 · Answer 6 · 2026-04-10 17:09:16

179

Views

Sufficient conditions for an element to be a unit in a euclidean domain

Published on 10 Apr 2026 - 17:09

score 38 · Answer 7 · 2026-04-12 22:07:11

38

Views

$A$ is a field iff $A[t]$ is euclidean.

Published on 12 Apr 2026 - 22:07

score 225 · Answer 8 · 2026-04-15 05:00:33

225

Views

How many quotients/remainders can we get for a given Gaussian integer?

Published on 15 Apr 2026 - 5:00

score 154 · Answer 9 · 2026-04-13 01:41:05

154

Views

Degree of the kernel of a module map $R^n\rightarrow R^n$ for an Euclidean domain $R$

Published on 13 Apr 2026 - 1:41

score 2.9k · Answer 10 · 2026-04-12 08:59:37

2.9k

Views

Show that every Euclidean ring is a principal ring

Published on 12 Apr 2026 - 8:59

score 117 · Answer 11 · 2026-04-15 16:50:06

117

Views

Why does Wolfram say domain of $y=\sqrt[3]{(x-1)^2(x+2)}$ is $x \in \mathcal{R} : x \ge 2$

Published on 15 Apr 2026 - 16:50

score 743 · Answer 12 · 2026-04-10 23:12:58

743

Views

Is $\mathbb{Z}[{ \sqrt 8 } ] $ a Euclidean domain?

Published on 10 Apr 2026 - 23:12

score 770 · Answer 13 · 2026-04-17 03:32:42

770

Views

$\mathbb{Z}[\sqrt{2}]$ is a euclidean domain

Published on 17 Apr 2026 - 3:32

score 431 · Answer 14 · 2026-04-15 04:42:14

431

Views

Prove that in an Euclidean domain, if $d(a) = 1$ then $a$ is invertible or irreducible

Published on 15 Apr 2026 - 4:42

score 84 · Answer 15 · 2026-04-16 11:27:55

84

Views

$m$ square-free integer such that $4\vert m-1\implies 2$ irreducible in $\mathbb{Z}[\sqrt{m}]$

Published on 16 Apr 2026 - 11:27

List Question

Visualizing euclidean rings

How to restrict only top range of ellipse function, and what is its domain?

Can anyone give me an example of an Euclidean Domain $D$ whose Euclidean Valuation at a point $a$: $v(a)$ is bigger than $\min \{v(ax) : x\in D\}$?

Can anyone gives me an example of $V$ such that there exists at least one pair of elements $ a,c(\neq 0 ,1) \in D$ such that $V(a) > V(ac)$

It is given that $a_1=\gcd(a_{11}, a_{12} , \cdots , a_{mn})$. Then prove that after elementary row and column operation we get ...

Sufficient conditions for an element to be a unit in a euclidean domain

$A$ is a field iff $A[t]$ is euclidean.

How many quotients/remainders can we get for a given Gaussian integer?

Degree of the kernel of a module map $R^n\rightarrow R^n$ for an Euclidean domain $R$

Show that every Euclidean ring is a principal ring

Why does Wolfram say domain of $y=\sqrt[3]{(x-1)^2(x+2)}$ is $x \in \mathcal{R} : x \ge 2$

Is $\mathbb{Z}[{ \sqrt 8 } ] $ a Euclidean domain?

$\mathbb{Z}[\sqrt{2}]$ is a euclidean domain

Prove that in an Euclidean domain, if $d(a) = 1$ then $a$ is invertible or irreducible

$m$ square-free integer such that $4\vert m-1\implies 2$ irreducible in $\mathbb{Z}[\sqrt{m}]$

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