List questions from principal-ideal-domains

Published on 20 Mar 2026 - 4:01

162

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How is the given set a basis for $K$?

Published on 26 Mar 2026 - 11:16

41

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Divisibility conditions

Published on 25 Mar 2026 - 14:39

1.5k

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Finding generator for Ideal generated by two elements in a PID

Published on 25 Mar 2026 - 23:09

593

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Principal Ideal Example

Published on 21 Mar 2026 - 19:17

33

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Commutative Rings: Principal Ideal Generator Question

Published on 22 Mar 2026 - 13:37

246

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Are $\mathbb C[x , y]$ and $ \frac {\mathbb R[x , y]}{ \left<x^2+1 , y\right>}$ PIDs?

Published on 07 May 2018 - 13:01

426

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In a principal ideal domain, gcd(a,b) always exists and can always be expressed as $xa +yb$ with some $x, y /in R$

Published on 25 Mar 2026 - 14:36

55

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On the structure of $R_0$ in graded PID $R=\bigoplus_{n \ge 0} R_n$

Published on 25 Mar 2026 - 4:42

344

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Element in a finitely generated torsion module on a PID with smallest non-zero annihilator

Published on 22 Mar 2026 - 17:43

82

Views

Identifying error in proof that $\mathbb{Q}_{\mathbb{Z}}[x]$ is a PID but not a UFD

Published on 25 Mar 2026 - 10:50

186

Views

Polynomial ring over a PID with infinitely many primes

Published on 19 Jun 2018 - 11:55

348

Views

Can a non-PID noetherian integral domain have all PID localizations?

Published on 25 Mar 2026 - 3:01

93

Views

Does Remak-Krull-Schmidt implies structure theorem for fg modules over PID

Published on 18 Jul 2018 - 13:28

29

Views

R is a PID(principal integral domain), and $pR+aR=cR$ then how can we say $p \in cR$?

Published on 21 Jul 2018 - 14:41

List Question

Definition of a Euclidean domain

How is the given set a basis for $K$?

Divisibility conditions

Finding generator for Ideal generated by two elements in a PID

Principal Ideal Example

Commutative Rings: Principal Ideal Generator Question

Are $\mathbb C[x , y]$ and $ \frac {\mathbb R[x , y]}{ \left<x^2+1 , y\right>}$ PIDs?

In a principal ideal domain, gcd(a,b) always exists and can always be expressed as $xa +yb$ with some $x, y /in R$

On the structure of $R_0$ in graded PID $R=\bigoplus_{n \ge 0} R_n$

Element in a finitely generated torsion module on a PID with smallest non-zero annihilator

Identifying error in proof that $\mathbb{Q}_{\mathbb{Z}}[x]$ is a PID but not a UFD

Polynomial ring over a PID with infinitely many primes

Can a non-PID noetherian integral domain have all PID localizations?

Does Remak-Krull-Schmidt implies structure theorem for fg modules over PID

R is a PID(principal integral domain), and $pR+aR=cR$ then how can we say $p \in cR$?

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