List questions from unique-factorization-domains

Published on 12 Apr 2026 - 19:39

476

Views

UFD and relatively prime elements

Published on 16 Apr 2026 - 21:24

557

Views

$q$ irreducible $\Longrightarrow$ $q/1$ irreducible or unit in localization $S^{-1}R$

Published on 16 Apr 2026 - 16:20

802

Views

Is a ring $R$ factorial $\iff$ $R[X]$ factorial?

Published on 14 Apr 2026 - 4:40

62

Views

Is there an example that a unit divisible by a prime element?

Published on 14 Apr 2026 - 1:31

231

Views

$R/\mathfrak p$ not always a UFD

Published on 13 Apr 2026 - 14:58

406

Views

Does any (noetherian) integral domain have a "UFD closure"?

Published on 14 Apr 2026 - 20:41

211

Views

Irreducible elements and unique factorization domain

Published on 14 Apr 2026 - 23:24

151

Views

$2=(a+b\sqrt{10})(c+d\sqrt{10})\implies 2=(a-b\sqrt{10})(c-d\sqrt{10})$

Published on 17 Apr 2026 - 2:04

1.8k

Views

Integral Domain but not a UFD

Published on 10 Apr 2026 - 17:45

147

Views

Show that $1-999x^{888}\in \mathbb{Q}[x]$ is irreducible

Published on 16 Apr 2026 - 14:59

118

Views

Unique factorization domain: existence of a complex number

Published on 14 Apr 2026 - 3:56

418

Views

Show $\mathbb{Z}_{(p)} [ \sqrt{D}]$ is a UFD

Published on 04 May 2026 - 21:04

52

Views

Finding an explicit factorisation

Published on 12 Apr 2026 - 17:00

1.6k

Views

Prove that $\mathbb{Z}$ is a UFD while $\mathbb{Z}[\sqrt{-5}]$ is not.

Published on 25 Mar 2026 - 18:49

List Question

Generalizing the Big Omega function to Integral Domains

UFD and relatively prime elements

$q$ irreducible $\Longrightarrow$ $q/1$ irreducible or unit in localization $S^{-1}R$

Is a ring $R$ factorial $\iff$ $R[X]$ factorial?

Is there an example that a unit divisible by a prime element?

$R/\mathfrak p$ not always a UFD

Does any (noetherian) integral domain have a "UFD closure"?

Irreducible elements and unique factorization domain

$2=(a+b\sqrt{10})(c+d\sqrt{10})\implies 2=(a-b\sqrt{10})(c-d\sqrt{10})$

Integral Domain but not a UFD

Show that $1-999x^{888}\in \mathbb{Q}[x]$ is irreducible

Unique factorization domain: existence of a complex number

Show $\mathbb{Z}_{(p)} [ \sqrt{D}]$ is a UFD

Finding an explicit factorisation

Prove that $\mathbb{Z}$ is a UFD while $\mathbb{Z}[\sqrt{-5}]$ is not.

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