List questions from principal-ideal-domains

Published on 27 Mar 2026 - 23:12

202

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Counterexample for a principal ring

Published on 26 Nov 2016 - 21:52

166

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Check whether $\mathbb{Q}[X_{1},X_{2},...]/(f_{1},f_{2},...)$ is a Bézout domain, Noetherian, Factorial, or PID

Published on 26 Mar 2026 - 19:03

747

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Ring epimorphism from principal ideal domain to integral domain.

Published on 11 Dec 2016 - 21:41

1.1k

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There are finitely many ideals containing $(a)$ in a PID

Published on 12 Dec 2016 - 18:51

77

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show that Ideal contains 1

Published on 12 Jan 2017 - 22:26

1.1k

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Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?

Published on 14 Jan 2017 - 0:05

313

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How do the elementary divisors of a matrix over a PID change if it is enlarged by a vector?

Published on 18 Jan 2017 - 13:37

430

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Is $\mathbb{Z}[t,t^{-1}]$ a PID? What about $\mathbb{Z}[\sqrt{2}i]$?

Published on 28 Mar 2026 - 20:57

417

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Why $R/J$ has finite ideals if $R$ PID?

Published on 25 Jan 2017 - 11:40

80

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Why $R\longrightarrow \bigoplus R/(q_i)$ is surjective?

Published on 27 Jan 2017 - 13:07

61

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Concerning a polynomial $f\in k[x,y]$ is not divisible by any non-constant polynomial of $k[x]$ nor of $k[y]$

Published on 28 Mar 2026 - 21:06

133

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Powers of distinct primes in PID are relatively prime

Published on 31 Jan 2017 - 3:24

48

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Dimension of a certain module over a field $R/\langle p \rangle$

Published on 01 Feb 2017 - 2:07

45

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Matrices over a PID with equal image only differ by an automorphism.

Published on 02 Feb 2017 - 11:57

List Question

Finitely generated modules over PID's

Counterexample for a principal ring

Check whether $\mathbb{Q}[X_{1},X_{2},...]/(f_{1},f_{2},...)$ is a Bézout domain, Noetherian, Factorial, or PID

Ring epimorphism from principal ideal domain to integral domain.

There are finitely many ideals containing $(a)$ in a PID

show that Ideal contains 1

Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?

How do the elementary divisors of a matrix over a PID change if it is enlarged by a vector?

Is $\mathbb{Z}[t,t^{-1}]$ a PID? What about $\mathbb{Z}[\sqrt{2}i]$?

Why $R/J$ has finite ideals if $R$ PID?

Why $R\longrightarrow \bigoplus R/(q_i)$ is surjective?

Concerning a polynomial $f\in k[x,y]$ is not divisible by any non-constant polynomial of $k[x]$ nor of $k[y]$

Powers of distinct primes in PID are relatively prime

Dimension of a certain module over a field $R/\langle p \rangle$

Matrices over a PID with equal image only differ by an automorphism.

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