List questions from principal-ideal-domains

Published on 28 Mar 2026 - 22:26

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Proof of every PID is Noetherian

Published on 29 Mar 2026 - 6:02

793

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Show that every ideal in the ring of Gaussian integers is principal

Published on 26 Mar 2026 - 9:47

708

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Locally Principal Ideal Domain

Published on 06 Sep 2020 - 23:50

119

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Ad hoc proof of Minkowski's bound for $\mathbb{Q}(\sqrt{-19})$

Published on 10 Sep 2020 - 17:18

354

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$(1-x,y)$ is not principal in $\Bbb Q[x,y]/(x^2+y^2-1)$

Published on 11 Sep 2020 - 8:22

128

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Polynomial Ring of a Field extension

Published on 13 Sep 2020 - 21:37

243

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In $\mathbb Z[x]$, show that the set $A$ of all polynomials with even constant term is not a principal ideal

Published on 16 Sep 2020 - 8:48

143

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A question about PIDs

Published on 16 Sep 2020 - 19:58

609

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Let $M$ be a free module over a PID with finite rank, then any submodule $N \subset M$ is also free with finite rank

Published on 17 Sep 2020 - 12:59

261

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Exact sequences and characteristic ideal of modules over a principal ideal domain

Published on 19 Sep 2020 - 8:02

45

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Computing $\operatorname{Aut}(\mathbb{C}[x]/(x-a)^n)$

Published on 31 Mar 2026 - 5:58

43

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Decomposition of finitely generated Module over PID

Published on 01 Oct 2020 - 5:15

534

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How to show that ${\Bbb Q}[x,y]/(x^2+y^2+1)$ is a PID?

Published on 01 Oct 2020 - 15:01

51

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Why does the ring element get absorbed here?

Published on 07 Oct 2020 - 3:28

List Question

What is principal ideal generated by $p$?

Proof of every PID is Noetherian

Show that every ideal in the ring of Gaussian integers is principal

Locally Principal Ideal Domain

Ad hoc proof of Minkowski's bound for $\mathbb{Q}(\sqrt{-19})$

$(1-x,y)$ is not principal in $\Bbb Q[x,y]/(x^2+y^2-1)$

Polynomial Ring of a Field extension

In $\mathbb Z[x]$, show that the set $A$ of all polynomials with even constant term is not a principal ideal

A question about PIDs

Let $M$ be a free module over a PID with finite rank, then any submodule $N \subset M$ is also free with finite rank

Exact sequences and characteristic ideal of modules over a principal ideal domain

Computing $\operatorname{Aut}(\mathbb{C}[x]/(x-a)^n)$

Decomposition of finitely generated Module over PID

How to show that ${\Bbb Q}[x,y]/(x^2+y^2+1)$ is a PID?

Why does the ring element get absorbed here?

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