List questions from principal-ideal-domains

Published on 13 Mar 2016 - 20:36

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Polynomial ring is not PID

Published on 15 Mar 2016 - 4:01

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Information about Problem. Let $a_1,\cdots,a_n\in\mathbb{Z}$ with $\gcd(a_1,\cdots,a_n)=1$. Then there exists a $n\times n$ matrix $A$ ...

Published on 28 Mar 2026 - 7:53

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When is the prime spectrum of a ring the finite complement topology on a set?

Published on 26 Mar 2026 - 9:42

64

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Domain of $\ln\left(\frac{6}{6+x-x^2}-1\right)+\arcsin\left(\frac{x+1}{3}\right)$

Published on 02 Apr 2016 - 17:11

174

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Showing that the integers localized at a prime, p, is a Euclidean Domain

Published on 28 Mar 2026 - 9:50

428

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Is a matrix over a PID similar to its transpose?

Published on 27 Mar 2026 - 5:37

1.2k

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Is $\mathbb{Q}[X,Y]/\langle X^2+Y^2-1\rangle$ a PID?

Published on 13 Apr 2016 - 6:05

104

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Show that there are finitely many different principal ideals

Published on 29 Mar 2026 - 17:24

2.8k

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A Bézout UFD is a PID.

Published on 28 Mar 2026 - 5:22

130

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Examples of PID's with finitely many maximal ideals

Published on 15 Apr 2016 - 16:19

88

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Let $A$ be a principal ideal domain, and $a,b,d$ elements of $A$. Prove that $d$ is a gcd of $a$ and $b$ if and only if $aA+bA=dA$.

Published on 16 Apr 2016 - 19:50

139

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Principal Ideal using coordinates?

Published on 22 Apr 2016 - 5:47

128

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On describing a sort of "well-behaved" subgroups of a free abelian group.

Published on 27 Mar 2026 - 5:39

1.7k

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Each proper ideal is a product of prime ideals

Published on 26 Apr 2016 - 16:41

List Question

Ideal generated by two monic polynomials in $\mathbb{Q}[x]$ and the GCD of their degrees

Polynomial ring is not PID

Information about Problem. Let $a_1,\cdots,a_n\in\mathbb{Z}$ with $\gcd(a_1,\cdots,a_n)=1$. Then there exists a $n\times n$ matrix $A$ ...

When is the prime spectrum of a ring the finite complement topology on a set?

Domain of $\ln\left(\frac{6}{6+x-x^2}-1\right)+\arcsin\left(\frac{x+1}{3}\right)$

Showing that the integers localized at a prime, p, is a Euclidean Domain

Is a matrix over a PID similar to its transpose?

Is $\mathbb{Q}[X,Y]/\langle X^2+Y^2-1\rangle$ a PID?

Show that there are finitely many different principal ideals

A Bézout UFD is a PID.

Examples of PID's with finitely many maximal ideals

Let $A$ be a principal ideal domain, and $a,b,d$ elements of $A$. Prove that $d$ is a gcd of $a$ and $b$ if and only if $aA+bA=dA$.

Principal Ideal using coordinates?

On describing a sort of "well-behaved" subgroups of a free abelian group.

Each proper ideal is a product of prime ideals

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