List questions from unique-factorization-domains

Published on 17 Dec 2015 - 1:03

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No irreducible element in a UFD can be a square.

Published on 07 Jan 2016 - 2:54

455

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Is $\mathbb{R}[x,y,z]/(x^2+y^2+z^2)$ a UFD?

Published on 10 Jan 2016 - 17:04

3k

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Is $\mathbb{Z}[\sqrt{15}]$ a UFD?

Published on 18 Jan 2016 - 13:13

1.6k

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Example of a UFD that is not Dedekind

Published on 26 Mar 2026 - 14:42

371

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Showing degree of algebraic closure is infinite

Published on 02 Mar 2016 - 0:11

987

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$x^3-9$ is irreducible over $\mathbb{Z}$

Published on 03 Mar 2016 - 0:40

127

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Understanding a solution to $m^3-n^2=2$

Published on 05 Mar 2016 - 1:28

1.5k

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A Noetherian integral domain is a UFD iff $(f):(g)$ is principal

Published on 28 Mar 2026 - 2:04

1.1k

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Is the property of being a UFD preserved under quotients by prime ideals?

Published on 27 Mar 2026 - 20:21

668

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Why are Unique Factorization Domains (UFD's) geometrically significant?

Published on 15 Mar 2016 - 5:06

712

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Show that in a UFD, prime elements are irreducible

Published on 17 Mar 2016 - 14:05

602

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Is a subring a UFD?

Published on 21 Mar 2016 - 6:54

113

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An example from Lang's Algebra about primary ideal

Published on 23 Mar 2016 - 22:30

1.8k

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Where Fermat's last theorem fails

Published on 27 Mar 2026 - 22:03

List Question

Is the ring of entire functions on $\mathbb C$ a UFD?

No irreducible element in a UFD can be a square.

Is $\mathbb{R}[x,y,z]/(x^2+y^2+z^2)$ a UFD?

Is $\mathbb{Z}[\sqrt{15}]$ a UFD?

Example of a UFD that is not Dedekind

Showing degree of algebraic closure is infinite

$x^3-9$ is irreducible over $\mathbb{Z}$

Understanding a solution to $m^3-n^2=2$

A Noetherian integral domain is a UFD iff $(f):(g)$ is principal

Is the property of being a UFD preserved under quotients by prime ideals?

Why are Unique Factorization Domains (UFD's) geometrically significant?

Show that in a UFD, prime elements are irreducible

Is a subring a UFD?

An example from Lang's Algebra about primary ideal

Where Fermat's last theorem fails

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