List questions from unique-factorization-domains

Published on 13 Apr 2026 - 1:24

57

Views

Example of a principal prime ideal containing a proper prime non-zero ideal.

Published on 15 Apr 2026 - 10:49

137

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Given $a, b$ coprime integers, show that any factor of $a^2 - 2b^2$ is of the form $c^2 - 2d^2$

Published on 10 May 2026 - 12:42

60

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Relationship between primes, irreducibles and UFDs and vacuously true

Published on 16 Apr 2026 - 20:57

89

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Unique factorization conjecture?

Published on 10 Apr 2026 - 23:39

175

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Ring with infinitely reducible elements

Published on 12 Apr 2026 - 5:39

51

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Irreducible element in a Integral domain

Published on 14 Apr 2026 - 20:15

495

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Prove $Z[\sqrt{7}]$ is euclidean domain

Published on 10 May 2026 - 12:41

288

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Question about the integral closure of adjoining a square root to a UFD?

Published on 11 Apr 2026 - 3:55

507

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Is content multiplicative if the ring is only integrally closed?

Published on 11 Apr 2026 - 21:37

48

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Factorisation of polynomials

Published on 12 Apr 2026 - 8:01

109

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Is $\mathbb{Z}[\sqrt{-5}]$ a factorization domain

Published on 10 Apr 2026 - 13:56

146

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Relation $ab=cd$ in $\mathbb{Z}$(UFD) with $a$ and $c$ coprime.

Published on 09 Apr 2026 - 3:53

40

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Rings that are UFD except for the fact that they are not integral domains.

Published on 16 Apr 2026 - 12:34

251

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Position of $\mathbb{Z}[\sqrt{-d}]$ in class hierarchy for all integers $d$

Published on 16 Apr 2026 - 4:24

List Question

$R$ a $PID \Rightarrow R[[X]]$ a $UFD$

Example of a principal prime ideal containing a proper prime non-zero ideal.

Given $a, b$ coprime integers, show that any factor of $a^2 - 2b^2$ is of the form $c^2 - 2d^2$

Relationship between primes, irreducibles and UFDs and vacuously true

Unique factorization conjecture?

Ring with infinitely reducible elements

Irreducible element in a Integral domain

Prove $Z[\sqrt{7}]$ is euclidean domain

Question about the integral closure of adjoining a square root to a UFD?

Is content multiplicative if the ring is only integrally closed?

Factorisation of polynomials

Is $\mathbb{Z}[\sqrt{-5}]$ a factorization domain

Relation $ab=cd$ in $\mathbb{Z}$(UFD) with $a$ and $c$ coprime.

Rings that are UFD except for the fact that they are not integral domains.

Position of $\mathbb{Z}[\sqrt{-d}]$ in class hierarchy for all integers $d$

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