Question

Do boundedly finite homotopy groups of a decreasing collection of Euclidean domains stabilize?

score 30 · Answer 1 · 2026-04-15 02:58:25

30

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Do boundedly finite homotopy groups of a decreasing collection of Euclidean domains stabilize?

Published on 15 Apr 2026 - 2:58

score 4.9k · Answer 2 · 2026-04-13 19:58:58

4.9k

Views

Euclidean domain: every irreducible element is prime

Published on 13 Apr 2026 - 19:58

score 40 · Answer 3 · 2026-04-15 20:40:47

40

Views

Short inequality proof on $\mathbb{Z}[\sqrt{-2}]$

Published on 15 Apr 2026 - 20:40

score 53 · Answer 4 · 2026-04-05 18:45:30

53

Views

Division in $\mathbb{Z}[i]$

Published on 05 Apr 2026 - 18:45

score 200 · Answer 5 · 2026-05-06 04:14:36

200

Views

Motivation of the definition of Euclidean Domain

Published on 06 May 2026 - 4:14

score 425 · Answer 6 · 2026-04-01 02:06:15

425

Views

Number of invertible elements in quotient ring

Published on 01 Apr 2026 - 2:06

score 349 · Answer 7 · 2026-05-06 12:10:51

349

Views

Prove that $R=\mathbb{Z}[i]$ is a Euclidean domain via $N(a+bi) = a^2+b^2. $

Published on 06 May 2026 - 12:10

score 3.8k · Answer 8 · 2026-04-11 09:53:14

3.8k

Views

Prove that $\mathbb{Z}[\sqrt{-2}]$ is a Euclidean domain and $\mathbb{Z}[\sqrt{-10}]$ is not

Published on 11 Apr 2026 - 9:53

score 1.4k · Answer 9 · 2026-04-13 20:04:03

1.4k

Views

Proof of: if A is an integral domain, then the units of A[x] are the constant polynomials that are units of A

Published on 13 Apr 2026 - 20:04

score 39 · Answer 10 · 2026-04-24 10:23:43

39

Views

Does anyone know when/in what work Dedekind introduced the concept of a Euclidean domain?

Published on 24 Apr 2026 - 10:23

score 189 · Answer 11 · 2026-04-01 00:51:55

189

Views

Proving rationals of the form $2^{-n}m$ are a Euclidean ring

Published on 01 Apr 2026 - 0:51

score 515 · Answer 12 · 2026-03-26 03:01:28

515

Views

Let $R$ be an integral domain and $p,q \in R$. Is it true that $(pq)R = pR \cap qR$?

Published on 26 Mar 2026 - 3:01

score 238 · Answer 13 · 2026-03-26 14:22:17

238

Views

Definition of a Euclidean Domain: how to show that the condition $f(ab)\ge f(a)$ is actually not necessary?

Published on 26 Mar 2026 - 14:22

score 68 · Answer 14 · 2026-03-26 14:19:39

68

Views

Closure and interior in subset topology

Published on 26 Mar 2026 - 14:19

score 130 · Answer 15 · 2026-03-26 14:21:09

130

Views

Prove that an ideal of a subring of $\mathbb{Q}$ is principal

Published on 26 Mar 2026 - 14:21

List Question

Do boundedly finite homotopy groups of a decreasing collection of Euclidean domains stabilize?

Euclidean domain: every irreducible element is prime

Short inequality proof on $\mathbb{Z}[\sqrt{-2}]$

Division in $\mathbb{Z}[i]$

Motivation of the definition of Euclidean Domain

Number of invertible elements in quotient ring

Prove that $R=\mathbb{Z}[i]$ is a Euclidean domain via $N(a+bi) = a^2+b^2. $

Prove that $\mathbb{Z}[\sqrt{-2}]$ is a Euclidean domain and $\mathbb{Z}[\sqrt{-10}]$ is not

Proof of: if A is an integral domain, then the units of A[x] are the constant polynomials that are units of A

Does anyone know when/in what work Dedekind introduced the concept of a Euclidean domain?

Proving rationals of the form $2^{-n}m$ are a Euclidean ring

Let $R$ be an integral domain and $p,q \in R$. Is it true that $(pq)R = pR \cap qR$?

Definition of a Euclidean Domain: how to show that the condition $f(ab)\ge f(a)$ is actually not necessary?

Closure and interior in subset topology

Prove that an ideal of a subring of $\mathbb{Q}$ is principal

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