List questions from unique-factorization-domains

Published on 09 Jun 2015 - 21:28

152

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Q($\sqrt[3]{2}$) - Unique Factorisation Domain?

Published on 30 Jun 2015 - 11:24

607

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converging power series over $p$-adic integers is a UFD

Published on 01 Jul 2015 - 17:29

142

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Notation for indexing the factorizations of a number?

Published on 01 Jul 2015 - 23:10

216

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Unique factorization domain: $\mathbb{Z}_{n}[x]$

Published on 04 Jul 2015 - 23:10

49

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Example of $S[1/a] \cong S[1/b]$ as rings via $\phi$, where $S$ is a UFD, $a, b \in S$, and $\phi(U(S)) \neq U(S)$.

Published on 01 Aug 2015 - 16:23

1.8k

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$R$ is a unique factorization domain $\iff$ every prime minimal over a principal ideal is also principal

Published on 03 Aug 2015 - 20:56

337

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Given $d \equiv 5 \pmod {10}$, prove $\mathcal{O}_{\mathbb{Q}(\sqrt{d})}$ never has unique factorization

Published on 27 Mar 2026 - 23:40

1.7k

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In a ring: If every non-zero and non-unit element factors into prime elements, is factorization over irreducible elements unique?

Published on 12 Aug 2015 - 8:51

315

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Perfect number in gaussian integers

Published on 26 Mar 2026 - 18:30

384

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Diophantine equation: $13^x+3=y^2$

Published on 26 Aug 2015 - 8:37

563

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A UFD for which the related formal power series ring is not a UFD

Published on 27 Mar 2026 - 4:58

547

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$(K[x,y,z]/(x^2+y^3+z^7))_{(x,y,z)}$ is a UFD.

Published on 06 Sep 2015 - 14:04

267

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Determine if $\mathbb{Z}[\sqrt{2}i]$ is UFD.

Published on 07 Sep 2015 - 20:52

62

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Primality of a two generated ideal (in a UFD).

Published on 08 Sep 2015 - 21:32

List Question

For which $d \in \mathbb{Z}$ is $\mathbb{Z}[\sqrt{d}]$ a unique factorization domain?

Q($\sqrt[3]{2}$) - Unique Factorisation Domain?

converging power series over $p$-adic integers is a UFD

Notation for indexing the factorizations of a number?

Unique factorization domain: $\mathbb{Z}_{n}[x]$

Example of $S[1/a] \cong S[1/b]$ as rings via $\phi$, where $S$ is a UFD, $a, b \in S$, and $\phi(U(S)) \neq U(S)$.

$R$ is a unique factorization domain $\iff$ every prime minimal over a principal ideal is also principal

Given $d \equiv 5 \pmod {10}$, prove $\mathcal{O}_{\mathbb{Q}(\sqrt{d})}$ never has unique factorization

In a ring: If every non-zero and non-unit element factors into prime elements, is factorization over irreducible elements unique?

Perfect number in gaussian integers

Diophantine equation: $13^x+3=y^2$

A UFD for which the related formal power series ring is not a UFD

$(K[x,y,z]/(x^2+y^3+z^7))_{(x,y,z)}$ is a UFD.

Determine if $\mathbb{Z}[\sqrt{2}i]$ is UFD.

Primality of a two generated ideal (in a UFD).

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