List questions from principal-ideal-domains

Published on 29 Mar 2026 - 20:54

111

Views

A question about annihilators of elements on modules over PID's

Published on 02 May 2017 - 22:18

60

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Given three polynomials $a(x), b(x)$, and $c(x)$ satisfying $\gcd(a(x), b(x), c(x))=1$

Published on 11 May 2017 - 10:02

313

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The form of elements in this particular principal ideal

Published on 20 May 2017 - 13:13

3.1k

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Submodules of finitely generated modules

Published on 04 Jun 2017 - 20:27

139

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Understanding the proof of gcd(a,b) being the last remainder in Euclidean algorithm

Published on 28 Mar 2026 - 22:08

145

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Prime ideals of $\mathbb{F}_p[X]$

Published on 13 Jun 2017 - 1:47

166

Views

Integral domains $R$ such that any ring $R \subset S \subset K$ is Noetherian

Published on 28 Mar 2026 - 10:16

513

Views

Euclid's Lemma in a PID: irreducibles are prime: $ \pi\mid ab\Rightarrow \pi\mid a\,$ or $\pi\mid b$

Published on 04 Jul 2017 - 14:02

100

Views

Refinement of the structure theorem of finitely generated modules over a principal ideal domain

Published on 29 Mar 2026 - 6:33

74

Views

Induced Isomorphism between Modules

Published on 11 Jul 2017 - 11:37

77

Views

If $A$ is a domain but not a field, then $(x)$ is not a maximal ideal of $A[x]$?

Published on 11 Jul 2017 - 16:35

1.2k

Views

Is $A=\Bbb Z[i] /(3+i)$ finite?

Published on 26 Mar 2026 - 6:05

175

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To check whether given ring is principal ideal domain?

Published on 17 Jul 2017 - 10:26

160

Views

Proving $I+J=R$ in a PID

Published on 19 Jul 2017 - 4:36

List Question

Showing that $2+\sqrt{-5}$ is not divisible by $3$ in $\mathbb{Z}[\sqrt{-5}]$

A question about annihilators of elements on modules over PID's

Given three polynomials $a(x), b(x)$, and $c(x)$ satisfying $\gcd(a(x), b(x), c(x))=1$

The form of elements in this particular principal ideal

Submodules of finitely generated modules

Understanding the proof of gcd(a,b) being the last remainder in Euclidean algorithm

Prime ideals of $\mathbb{F}_p[X]$

Integral domains $R$ such that any ring $R \subset S \subset K$ is Noetherian

Euclid's Lemma in a PID: irreducibles are prime: $ \pi\mid ab\Rightarrow \pi\mid a\,$ or $\pi\mid b$

Refinement of the structure theorem of finitely generated modules over a principal ideal domain

Induced Isomorphism between Modules

If $A$ is a domain but not a field, then $(x)$ is not a maximal ideal of $A[x]$?

Is $A=\Bbb Z[i] /(3+i)$ finite?

To check whether given ring is principal ideal domain?

Proving $I+J=R$ in a PID

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