List questions from principal-ideal-domains

Published on 07 Oct 2020 - 21:32

506

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Are quotients of a PID by non-prime ideals ever a PID?

Published on 08 Oct 2020 - 11:52

185

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Maximal free submodule over a PID

Published on 13 Oct 2020 - 8:59

615

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Proof that Divisible Modules are Injective over a PID

Published on 27 Mar 2026 - 16:20

92

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Which element belong to the principal ideal $(3+i)$?

Published on 14 Oct 2020 - 20:24

197

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What condition makes $\mathbb{Z}[a]$ is PID, where $a$ is complex number.

Published on 22 Oct 2020 - 15:27

99

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Isomorphism between posets of ideals of $\mathbb Q[x]$ and $\mathbb Q[x,y]$.

Published on 30 Mar 2026 - 8:57

43

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How to prove $ y_1, \dots , y_n$ generate module M？

Published on 02 Nov 2020 - 11:11

136

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Uniqueness of a Decomposition of a finitely generated torsion module over a PID

Published on 04 Nov 2020 - 21:04

163

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Reference on different types of integral domains

Published on 29 Mar 2026 - 4:48

1k

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Let $F$ be an infinite field and let $f(x) ∈ F[x]$. If $f(a) = 0$ for infinitely many $a ∈ F$, show that $f = 0$.

Published on 23 Feb 2026 - 8:28

24

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Prove that $x = uy$ for some unit $u \in R^{\times}$ iff $(x)=(y)$ as ideals.

Published on 16 Nov 2020 - 15:28

163

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Units in a ring between an integral domain $R$ and its fraction field.

Published on 16 Nov 2020 - 20:06

189

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In a PID $R$, given $a,b\in R$, what are the ideals $\langle a\rangle,\langle b\rangle$ also generated by?

Published on 19 Nov 2020 - 5:02

117

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Why irreduciblilty and not division leads to relative primeness in a PID

Published on 29 Nov 2020 - 5:31

List Question

What is the dimension of this vector space?

Are quotients of a PID by non-prime ideals ever a PID?

Maximal free submodule over a PID

Proof that Divisible Modules are Injective over a PID

Which element belong to the principal ideal $(3+i)$?

What condition makes $\mathbb{Z}[a]$ is PID, where $a$ is complex number.

Isomorphism between posets of ideals of $\mathbb Q[x]$ and $\mathbb Q[x,y]$.

How to prove $ y_1, \dots , y_n$ generate module M？

Uniqueness of a Decomposition of a finitely generated torsion module over a PID

Reference on different types of integral domains

Let $F$ be an infinite field and let $f(x) ∈ F[x]$. If $f(a) = 0$ for infinitely many $a ∈ F$, show that $f = 0$.

Prove that $x = uy$ for some unit $u \in R^{\times}$ iff $(x)=(y)$ as ideals.

Units in a ring between an integral domain $R$ and its fraction field.

In a PID $R$, given $a,b\in R$, what are the ideals $\langle a\rangle,\langle b\rangle$ also generated by?

Why irreduciblilty and not division leads to relative primeness in a PID

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