Question

Visualizing euclidean rings

score 156 · Answer 1 · 2026-03-25 09:22:09

156

Views

Visualizing euclidean rings

Published on 25 Mar 2026 - 9:22

score 588 · Answer 2 · 2026-03-25 12:54:54

588

Views

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

Published on 25 Mar 2026 - 12:54

score 88 · Answer 3 · 2019-04-22 08:39:46

88

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 22 Apr 2019 - 8:39

score 27 · Answer 4 · 2019-04-22 14:37:41

27

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 22 Apr 2019 - 14:37

score 220 · Answer 5 · 2026-02-23 06:03:56

220

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 23 Feb 2026 - 6:03

score 177 · Answer 6 · 2026-03-25 16:02:07

177

Views

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

Published on 25 Mar 2026 - 16:02

score 35 · Answer 7 · 2019-06-09 10:27:25

35

Views

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

Published on 09 Jun 2019 - 10:27

score 223 · Answer 8 · 2026-03-25 07:49:14

223

Views

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

Published on 25 Mar 2026 - 7:49

score 151 · Answer 9 · 2019-06-25 10:44:19

151

Views

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

Published on 25 Jun 2019 - 10:44

score 2.9k · Answer 10 · 2019-07-15 13:15:50

2.9k

Views

Show that every Euclidean ring is a principal ring

Published on 15 Jul 2019 - 13:15

score 114 · Answer 11 · 2019-08-22 10:15:57

114

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 22 Aug 2019 - 10:15

score 740 · Answer 12 · 2019-08-25 19:33:06

740

Views

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

Published on 25 Aug 2019 - 19:33

score 766 · Answer 13 · 2026-03-25 12:24:17

766

Views

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

Published on 25 Mar 2026 - 12:24

score 429 · Answer 14 · 2019-09-09 01:39:25

429

Views

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

Published on 09 Sep 2019 - 1:39

score 82 · Answer 15 · 2026-03-25 21:48:16

82

Views

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

Published on 25 Mar 2026 - 21:48

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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