List questions from principal-ideal-domains

Published on 03 Apr 2020 - 9:12

377

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Show that any non zero ideal of a principal ideal domain is a unique product of prime ideals

Published on 04 Apr 2020 - 8:33

73

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Question about integer number and PID

Published on 06 Apr 2020 - 17:47

762

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Cyclic Modules over a PID

Published on 07 Apr 2020 - 6:03

127

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Does being principal ideal ring with identity implies PID?

Published on 26 Mar 2026 - 4:29

90

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Given a nonconstant $f\in \Bbb C[x]$, condition for every finitely generated indecomposable $\Bbb C[x]/(f)$-module is projective

Published on 12 Apr 2020 - 0:48

409

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Isn't $I$ a maximal ideal in $\Bbb Z_{11} [X]$?

Published on 12 Apr 2020 - 5:43

170

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In what rings is every ideal a fractional ideal?

Published on 12 Apr 2020 - 10:21

394

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Let $A$ be a PID, $M$ an injective finitely generated module. Prove that $M = 0$.

Published on 26 Mar 2026 - 14:29

794

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Is $\Bbb Z / n \Bbb Z$ a PID?

Published on 19 Apr 2020 - 22:10

179

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Let $R$ be a PID, and let $\pi\in R$ be prime. Is it $R/\langle\pi\rangle \times R/\langle \pi\rangle$ a cyclic $R$-module?

Published on 22 Apr 2020 - 19:35

79

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Intersection of two principal ideals in an integral domain.

Published on 01 May 2020 - 2:08

508

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Why is the polynomial ring $\Bbb R[x]$ a PID but $\Bbb Z[x]$ is not?

Published on 03 May 2020 - 19:57

58

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Counter-example Modules

Published on 12 May 2020 - 19:06

371

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Use of "$A$ is a domain" in the proof that $Q$ is an injective $A$-module iff it is divisible

Published on 26 Mar 2026 - 14:31

List Question

Find necessary and sufficent condition question

Show that any non zero ideal of a principal ideal domain is a unique product of prime ideals

Question about integer number and PID

Cyclic Modules over a PID

Does being principal ideal ring with identity implies PID?

Given a nonconstant $f\in \Bbb C[x]$, condition for every finitely generated indecomposable $\Bbb C[x]/(f)$-module is projective

Isn't $I$ a maximal ideal in $\Bbb Z_{11} [X]$?

In what rings is every ideal a fractional ideal?

Let $A$ be a PID, $M$ an injective finitely generated module. Prove that $M = 0$.

Is $\Bbb Z / n \Bbb Z$ a PID?

Let $R$ be a PID, and let $\pi\in R$ be prime. Is it $R/\langle\pi\rangle \times R/\langle \pi\rangle$ a cyclic $R$-module?

Intersection of two principal ideals in an integral domain.

Why is the polynomial ring $\Bbb R[x]$ a PID but $\Bbb Z[x]$ is not?

Counter-example Modules

Use of "$A$ is a domain" in the proof that $Q$ is an injective $A$-module iff it is divisible

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