Question

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

score 27 · Answer 1 · 2019-09-12 11:04:26

27

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

Published on 12 Sep 2019 - 11:04

score 4.9k · Answer 2 · 2014-09-28 21:19:41

4.9k

Views

Euclidean domain: every irreducible element is prime

Published on 28 Sep 2014 - 21:19

score 38 · Answer 3 · 2019-10-20 21:33:37

38

Views

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

Published on 20 Oct 2019 - 21:33

score 51 · Answer 4 · 2019-10-23 09:48:50

51

Views

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

Published on 23 Oct 2019 - 9:48

score 198 · Answer 5 · 2019-10-24 11:17:23

198

Views

Motivation of the definition of Euclidean Domain

Published on 24 Oct 2019 - 11:17

score 423 · Answer 6 · 2019-11-01 01:14:04

423

Views

Number of invertible elements in quotient ring

Published on 01 Nov 2019 - 1:14

score 348 · Answer 7 · 2019-11-09 20:46:29

348

Views

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

Published on 09 Nov 2019 - 20:46

score 3.8k · Answer 8 · 2026-03-24 22:19:42

3.8k

Views

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

Published on 24 Mar 2026 - 22:19

score 1.4k · Answer 9 · 2019-11-21 19:21:48

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 21 Nov 2019 - 19:21

score 34 · Answer 10 · 2026-03-24 22:04:44

34

Views

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

Published on 24 Mar 2026 - 22:04

score 188 · Answer 11 · 2026-03-18 13:30:03

188

Views

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

Published on 18 Mar 2026 - 13:30

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 237 · Answer 13 · 2020-01-04 04:43:17

237

Views

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

Published on 04 Jan 2020 - 4:43

score 67 · Answer 14 · 2020-01-22 16:39:21

67

Views

Closure and interior in subset topology

Published on 22 Jan 2020 - 16:39

score 129 · Answer 15 · 2020-01-24 23:22:26

129

Views

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

Published on 24 Jan 2020 - 23:22

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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