List questions from unique-factorization-domains

Published on 06 Feb 2024 - 3:37

67

Views

Explicit proof of the fact that a domain which is not a UFD is not a PID

Published on 12 Feb 2024 - 11:40

316

Views

Are there rings where factorization is unique, but does not necessarily exist?

Published on 11 Mar 2024 - 12:47

58

Views

Factorization Question

Published on 04 Jan 2015 - 18:10

3.4k

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Ring of formal power series over a principal ideal domain is a unique factorisation domain

Published on 27 Mar 2026 - 7:18

1k

Views

What's wrong with this proof that all UFDs are Bezout?

Published on 11 Jan 2015 - 0:45

2.6k

Views

Prove that $a+ib$ is prime in $\Bbb Z[i]$, if $a^2+b^2$ is prime in $\Bbb Z$.

Published on 26 Jan 2015 - 12:14

127

Views

Integrally closed domain.

Published on 27 Jan 2015 - 1:58

143

Views

Unique factorisation in ring generated by square roots of prime numbers?

Published on 02 Feb 2015 - 10:12

366

Views

How to show $\mathbb{Z}[\sqrt{-5}]_2$ is a UFD?

Published on 12 Feb 2015 - 1:01

327

Views

What is an example of UFD such that a gcd of an infinite set does not exist?

Published on 21 Feb 2015 - 6:33

1.9k

Views

Why is the ring $\mathbb{Z}[2\sqrt{2}]$ not a unique factorization domain?

Published on 05 Mar 2015 - 16:53

102

Views

How to go about proving that $-1+(x-4)(x-3)(x-2)(x-1)$ is irreducible in $\mathbb{Q}$?

Published on 05 Mar 2015 - 17:46

1.1k

Views

A UFD is a PID if Bezout (every ideal $(a,b)=(c)$ is principal)

Published on 11 Mar 2015 - 14:44

2.3k

Views

Is a height one ideal in a UFD principal?

Published on 12 Mar 2015 - 5:58

List Question

Need help understanding the proof showing the existence of gcd in an UFD.

Explicit proof of the fact that a domain which is not a UFD is not a PID

Are there rings where factorization is unique, but does not necessarily exist?

Factorization Question

Ring of formal power series over a principal ideal domain is a unique factorisation domain

What's wrong with this proof that all UFDs are Bezout?

Prove that $a+ib$ is prime in $\Bbb Z[i]$, if $a^2+b^2$ is prime in $\Bbb Z$.

Integrally closed domain.

Unique factorisation in ring generated by square roots of prime numbers?

How to show $\mathbb{Z}[\sqrt{-5}]_2$ is a UFD?

What is an example of UFD such that a gcd of an infinite set does not exist?

Why is the ring $\mathbb{Z}[2\sqrt{2}]$ not a unique factorization domain?

How to go about proving that $-1+(x-4)(x-3)(x-2)(x-1)$ is irreducible in $\mathbb{Q}$?

A UFD is a PID if Bezout (every ideal $(a,b)=(c)$ is principal)

Is a height one ideal in a UFD principal?

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