List questions from unique-factorization-domains

Published on 17 Jun 2016 - 9:30

116

Views

A question on part of the proof of the theorem that if $R$ is a UFD then $R[x]$ is a UFD as well.

Published on 21 Jun 2016 - 6:58

319

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Let $D$ be a UFD. If an element of $D$ is not a square in $D$ then is it true that it is not a square in the fraction field of $D$?

Published on 28 Mar 2026 - 3:03

843

Views

How do I prove that $\mathbb{Z}[\sqrt{19}]$ is not a UFD?

Published on 23 Feb 2026 - 3:58

612

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Ideals of Unique Factorization Domain

Published on 29 Jun 2016 - 7:17

3.8k

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Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.

Published on 03 Apr 2013 - 20:50

185

Views

How to show that $\mathbb{C}[x,y]/\langle y^2-P(x)\rangle$ is not a UFD (unique factorization domain)?

Published on 08 Apr 2013 - 15:31

1.3k

Views

Subring of $\mathbb Z[x]$ is UFD or not?

Published on 14 Apr 2013 - 18:34

176

Views

square-root of a square-free element (Matsumura)

Published on 17 Apr 2013 - 13:45

414

Views

How does Local Cohomology detect UFD?

Published on 25 Mar 2026 - 11:00

555

Views

GCD in a subring is GCD in a bigger ring?

Published on 07 May 2013 - 7:30

4.1k

Views

When a quotient of a UFD is also a UFD?

Published on 27 May 2013 - 6:28

567

Views

Is $k[x,y,z]/(x^2+y^2-z^2)$ a UFD?

Published on 07 Jun 2013 - 2:07

2.2k

Views

Quotient ring is a UFD

Published on 05 Sep 2013 - 18:20

4.8k

Views

Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain

Published on 21 Sep 2013 - 15:46

List Question

Why can we interchange "primes" and "irreducibles" in the definition of UFD?

A question on part of the proof of the theorem that if $R$ is a UFD then $R[x]$ is a UFD as well.

Let $D$ be a UFD. If an element of $D$ is not a square in $D$ then is it true that it is not a square in the fraction field of $D$?

How do I prove that $\mathbb{Z}[\sqrt{19}]$ is not a UFD?

Ideals of Unique Factorization Domain

Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.

How to show that $\mathbb{C}[x,y]/\langle y^2-P(x)\rangle$ is not a UFD (unique factorization domain)?

Subring of $\mathbb Z[x]$ is UFD or not?

square-root of a square-free element (Matsumura)

How does Local Cohomology detect UFD?

GCD in a subring is GCD in a bigger ring?

When a quotient of a UFD is also a UFD?

Is $k[x,y,z]/(x^2+y^2-z^2)$ a UFD?

Quotient ring is a UFD

Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain

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