List questions from unique-factorization-domains

Published on 26 Mar 2026 - 3:11

738

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Example of a domain where all irreducibles are primes and that is not a GCD domain

Published on 21 Apr 2015 - 13:23

2.2k

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Let $q$ be a prime congruent to 3 mod 4, prove the quotient ring $\mathbb{Z}[i]/(q)$ is a field with $q^2$ elements

Published on 27 Mar 2026 - 18:27

75

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Cardinality of a UFD

Published on 27 Apr 2015 - 22:47

2.9k

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If in a UFD every maximal ideal is principal then it is a PID

Published on 02 May 2015 - 14:47

3.7k

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Is a polynomial ring over a UFD in countably many variables a UFD?

Published on 04 May 2015 - 17:46

29

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A paper on the relation between Ernst Kummer's work on factorization and structural linguistics (Zellig Harris)

Published on 08 May 2015 - 10:55

423

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Where does the proof of unique factorization fail for $\mathbb Z[\sqrt{-5}]$?

Published on 11 May 2015 - 8:47

58

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Number Theory/Quadratic Number Rings

Published on 18 May 2015 - 12:44

975

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Gauss's lemma: More than a stepping stone on the way to proving $R[x]$ is a UFD when $R$ is?

Published on 19 May 2015 - 6:41

581

Views

Proof of No Unique Factorisation in $\mathbb Z[\sqrt{d}]$ for $d \leq-3$

Published on 19 May 2015 - 18:37

1.9k

Views

About the ways prove that a ring is a UFD.

Published on 20 May 2015 - 8:13

256

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Is a smooth ring extension of a UFD a UFD?

Published on 26 May 2015 - 2:57

1k

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How does one prove that $\mathbb{Z}\left[\frac{1 + \sqrt{-43}}{2}\right]$ is a unique factorization domain?

Published on 27 May 2015 - 1:39

3.3k

Views

Show that $\mathbb{C}[x,y]/(x^2+y^2-1)$ is a UFD.

Published on 04 Jun 2015 - 7:54

List Question

A UFD is a PID if it has dimension $\le 1$ (nonzero prime ideals are maximal)

Example of a domain where all irreducibles are primes and that is not a GCD domain

Let $q$ be a prime congruent to 3 mod 4, prove the quotient ring $\mathbb{Z}[i]/(q)$ is a field with $q^2$ elements

Cardinality of a UFD

If in a UFD every maximal ideal is principal then it is a PID

Is a polynomial ring over a UFD in countably many variables a UFD?

A paper on the relation between Ernst Kummer's work on factorization and structural linguistics (Zellig Harris)

Where does the proof of unique factorization fail for $\mathbb Z[\sqrt{-5}]$?

Number Theory/Quadratic Number Rings

Gauss's lemma: More than a stepping stone on the way to proving $R[x]$ is a UFD when $R$ is?

Proof of No Unique Factorisation in $\mathbb Z[\sqrt{d}]$ for $d \leq-3$

About the ways prove that a ring is a UFD.

Is a smooth ring extension of a UFD a UFD?

How does one prove that $\mathbb{Z}\left[\frac{1 + \sqrt{-43}}{2}\right]$ is a unique factorization domain?

Show that $\mathbb{C}[x,y]/(x^2+y^2-1)$ is a UFD.

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