Question

What are some simple examples of "ID-only" rings? integral domains, that are neither atomic nor Noether nor Prüfer...

score 60 · Answer 1 · 2026-03-29 14:59:15

60

Views

What are some simple examples of "ID-only" rings? integral domains, that are neither atomic nor Noether nor Prüfer...

Published on 29 Mar 2026 - 14:59

score 154 · Answer 2 · 2022-01-25 23:22:53

154

Views

Why must the norm of a prime element in a UFD be either a prime number or a prime number squared?

Published on 25 Jan 2022 - 23:22

score 52 · Answer 3 · 2026-03-29 14:57:34

52

Views

Irreducible polynomials over non-UFD

Published on 29 Mar 2026 - 14:57

score 261 · Answer 4 · 2022-02-24 15:54:55

261

Views

Finding the $\gcd$ of two polynomials over $\Bbb Z[x]$

Published on 24 Feb 2022 - 15:54

score 106 · Answer 5 · 2026-03-26 12:36:35

106

Views

What are the integers that lack unique factorization in $\mathbb Z[\zeta_n],$ $n= 23$?

Published on 26 Mar 2026 - 12:36

score 856 · Answer 6 · 2022-03-09 00:56:42

856

Views

Let $R:=\mathbb{Z}[\sqrt{-6}]$. Prove that $R$ is not a Unique Factorization Domain

Published on 09 Mar 2022 - 0:56

score 129 · Answer 7 · 2022-03-27 15:42:53

129

Views

Show that the ring $\mathbb C[x^3,x^2y,xy^2,y^3]$ is normal, but it is not a unique factorisation domain

Published on 27 Mar 2022 - 15:42

score 733 · Answer 8 · 2022-04-23 22:47:15

733

Views

How can an irreducible polynomial be represented as a product of irreducible polynomials?

Published on 23 Apr 2022 - 22:47

score 160 · Answer 9 · 2022-05-24 04:19:56

160

Views

Is $\mathbb{Z}[\sqrt[3]{2}]$ a UFD?

Published on 24 May 2022 - 4:19

score 119 · Answer 10 · 2026-03-25 19:10:42

119

Views

Finding $x$ from $Ax = b$ with $QR$ factorization

Published on 25 Mar 2026 - 19:10

score 63 · Answer 11 · 2022-05-26 11:47:16

63

Views

Minimal non-zero prime ideal in a UFD

Published on 26 May 2022 - 11:47

score 263 · Answer 12 · 2022-06-07 17:02:58

263

Views

Problem in understanding of If $R$ is a UFD, then $R[x]$ is also a UFD(Gauss's theorem)

Published on 07 Jun 2022 - 17:02

score 40 · Answer 13 · 2022-06-15 09:06:51

40

Views

Is it true that an uniformizing element of a discrete valuation ring $R$ is either zero or prime?

Published on 15 Jun 2022 - 9:06

score 208 · Answer 14 · 2022-07-01 13:28:33

208

Views

Is $\mathbb R[X,Y,Z]/(X^2+Y^2+Z^2+1)$ a unique factorization domain?

Published on 01 Jul 2022 - 13:28

score 293 · Answer 15 · 2026-03-29 16:32:14

293

Views

Number of ring structures on $\mathbb{Z}$ with the usual multiplication

Published on 29 Mar 2026 - 16:32

List Question

What are some simple examples of "ID-only" rings? integral domains, that are neither atomic nor Noether nor Prüfer...

Why must the norm of a prime element in a UFD be either a prime number or a prime number squared?

Irreducible polynomials over non-UFD

Finding the $\gcd$ of two polynomials over $\Bbb Z[x]$

What are the integers that lack unique factorization in $\mathbb Z[\zeta_n],$ $n= 23$?

Let $R:=\mathbb{Z}[\sqrt{-6}]$. Prove that $R$ is not a Unique Factorization Domain

Show that the ring $\mathbb C[x^3,x^2y,xy^2,y^3]$ is normal, but it is not a unique factorisation domain

How can an irreducible polynomial be represented as a product of irreducible polynomials?

Is $\mathbb{Z}[\sqrt[3]{2}]$ a UFD?

Finding $x$ from $Ax = b$ with $QR$ factorization

Minimal non-zero prime ideal in a UFD

Problem in understanding of If $R$ is a UFD, then $R[x]$ is also a UFD(Gauss's theorem)

Is it true that an uniformizing element of a discrete valuation ring $R$ is either zero or prime?

Is $\mathbb R[X,Y,Z]/(X^2+Y^2+Z^2+1)$ a unique factorization domain?

Number of ring structures on $\mathbb{Z}$ with the usual multiplication

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