List questions from euclidean-domain

Published on 25 Mar 2026 - 13:59

232

Views

Limitations that make a simple euclidean space a Hilbert space

Published on 06 Dec 2016 - 9:00

64

Views

Proof for existence of integer order for non-zero elements in Euclidian domain

Published on 28 Dec 2016 - 4:53

106

Views

Topology on Euclidean space

Published on 05 Feb 2017 - 11:51

121

Views

About characterizations of Euclidean Domains

Published on 11 Feb 2017 - 15:25

307

Views

The Set of Zeros of an Ideal Generated by Two Irreducible Polynomials in $\mathbb{A}^2$

Published on 12 Feb 2017 - 10:19

40

Views

A question of Euclidean domain

Published on 24 Feb 2017 - 4:56

1.9k

Views

Uniqueness of the remainder and quotient in an Euclidean domain

Published on 04 Mar 2017 - 17:19

6.9k

Views

Euclidean domain $\mathbb{Z}[\sqrt{d}]$

Published on 18 Mar 2017 - 17:01

2k

Views

$\mathbb{Z}[\sqrt{11}]$ is norm-euclidean

Published on 02 Apr 2017 - 21:14

18

Views

Suppose $R$ is an integral domain, $a, b\in R$ are nonzero. Suppose $x$ is nonzero, then $x\in(a, b)$ IFF $x=sa-tb$ for some $s, t\in R$.

Published on 09 Feb 2023 - 0:08

601

Views

Show that the quadratic integer ring $\mathcal{O}=\{a+b\frac{1+\sqrt{-3}}{2}|a, b\in\mathbb{Z}\}$ is an Euclidean Domain.

Published on 09 Feb 2023 - 23:23

108

Views

If $p\in\mathbb{Z}$ is a prime and $p\equiv 1$ mod $4$, show that the quotient ring $\mathbb{Z}[i]/(p)$ has order $p^2$.

Published on 26 Mar 2026 - 1:23

47

Views

Is the quotient by a unit in an euclidean domain unique?

Published on 30 Mar 2023 - 2:34

44

Views

Condition on the remainder in an Euclidean domain

Published on 10 Apr 2023 - 21:05

List Question

Is all Euclidean domain local?

Limitations that make a simple euclidean space a Hilbert space

Proof for existence of integer order for non-zero elements in Euclidian domain

Topology on Euclidean space

About characterizations of Euclidean Domains

The Set of Zeros of an Ideal Generated by Two Irreducible Polynomials in $\mathbb{A}^2$

A question of Euclidean domain

Uniqueness of the remainder and quotient in an Euclidean domain

Euclidean domain $\mathbb{Z}[\sqrt{d}]$

$\mathbb{Z}[\sqrt{11}]$ is norm-euclidean

Suppose $R$ is an integral domain, $a, b\in R$ are nonzero. Suppose $x$ is nonzero, then $x\in(a, b)$ IFF $x=sa-tb$ for some $s, t\in R$.

Show that the quadratic integer ring $\mathcal{O}=\{a+b\frac{1+\sqrt{-3}}{2}|a, b\in\mathbb{Z}\}$ is an Euclidean Domain.

If $p\in\mathbb{Z}$ is a prime and $p\equiv 1$ mod $4$, show that the quotient ring $\mathbb{Z}[i]/(p)$ has order $p^2$.

Is the quotient by a unit in an euclidean domain unique?

Condition on the remainder in an Euclidean domain

Trending Questions

Popular # Hahtags

Popular Questions