List questions from principal-ideal-domains

Published on 19 Nov 2012 - 20:19

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Ring of trigonometric functions with real coefficients

Published on 30 Mar 2026 - 7:07

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Show that $\mathbb{Z}[\theta]$ (where $\theta = (1 + \sqrt{19}i)/2$) is a principal ideal domain.

Published on 29 Nov 2012 - 3:20

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Domain of a complex function

Published on 24 Jan 2013 - 4:30

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For which $d$ is $\mathbb Z[\sqrt d]$ a principal ideal domain?

Published on 05 Mar 2013 - 9:45

501

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which of the following statements are true and why?

Published on 07 Mar 2013 - 15:02

501

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Show that $\mathbb{Z}[x]=\lbrace \sum_{i=0}^{n}{a_ix^i}:a_i \in \mathbb{Z}, n \geq 0 \rbrace$ is not a principal ideal ring.

Published on 25 Mar 2013 - 20:13

778

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If $R$ is an Euclidean domain that is not a field, is $R[X]$ a PID?

Published on 02 Aug 2020 - 12:47

61

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Prove that $\mathbb{Q}[X,Y] $ / (X) is a PID

Published on 08 Aug 2020 - 7:38

122

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In a PID show that $(ab)=(a)\cap(b)$ $\iff$ $(a)+(b)=1$

Published on 08 Aug 2020 - 14:01

294

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Prove $(7)$ is maximal in Gaussian Integers

Published on 26 Mar 2026 - 11:06

407

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Fraction field of $\mathbb Z_p[[X]]$

Published on 19 Aug 2020 - 16:39

141

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If any ideal in $R$ is principal, then any ideal in $R \times R$ is principal

Published on 30 Aug 2020 - 22:33

218

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Question about Principal ring

Published on 31 Aug 2020 - 14:04

177

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uncountable principal ideal domain with few units

Published on 02 Sep 2020 - 8:07

List Question

Units in $\mathbb{Z}[\sqrt[3]{2}]$ : $\pm(1+\sqrt[3]{2}+(\sqrt[3]{2})^2)^n$?

Ring of trigonometric functions with real coefficients

Show that $\mathbb{Z}[\theta]$ (where $\theta = (1 + \sqrt{19}i)/2$) is a principal ideal domain.

Domain of a complex function

For which $d$ is $\mathbb Z[\sqrt d]$ a principal ideal domain?

which of the following statements are true and why?

Show that $\mathbb{Z}[x]=\lbrace \sum_{i=0}^{n}{a_ix^i}:a_i \in \mathbb{Z}, n \geq 0 \rbrace$ is not a principal ideal ring.

If $R$ is an Euclidean domain that is not a field, is $R[X]$ a PID?

Prove that $\mathbb{Q}[X,Y] $ / (X) is a PID

In a PID show that $(ab)=(a)\cap(b)$ $\iff$ $(a)+(b)=1$

Prove $(7)$ is maximal in Gaussian Integers

Fraction field of $\mathbb Z_p[[X]]$

If any ideal in $R$ is principal, then any ideal in $R \times R$ is principal

Question about Principal ring

uncountable principal ideal domain with few units

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