List questions from principal-ideal-domains

Published on 01 May 2012 - 7:11

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Show that the ring of all rational numbers, which when written in simplest form has an odd denominator, is a principal ideal domain.

Published on 31 Mar 2026 - 10:57

1.7k

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If two elements in a ED have the same Euclidean norm, are they associates?

Published on 29 Mar 2026 - 7:32

1.2k

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Ring of analytic functions on the circle

Published on 29 Mar 2026 - 18:33

17.6k

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Submodule of free module over a p.i.d. is free even when the module is not finitely generated?

Published on 25 Jun 2012 - 18:21

734

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Integer extensions, rings $\mathbb{Z}[\sqrt{s}]$

Published on 26 Jun 2012 - 19:20

984

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Question about torsion submodules and Decomposition theorem

Published on 04 Jul 2012 - 23:42

16.8k

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An integral domain whose every prime ideal is principal is a PID

Published on 08 Jul 2012 - 1:12

3.7k

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Every prime ideal is either zero or maximal in a PID.

Published on 08 Jul 2012 - 2:38

989

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Exercise on modules over PID involving injective modules, Baer's criterion. (Exercise IV.6.7 in Hungerford's Algebra)

Published on 09 Jul 2012 - 17:39

231

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Is $(x^3-x^2+2x-1)$ prime in $\mathbb{Z}/(3)[x]$?

Published on 14 Jul 2012 - 1:54

157

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Reference on Operators on Modules over PID

Published on 17 Jul 2012 - 3:00

2.4k

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How does a Class group measure the failure of Unique factorization?

Published on 28 Mar 2026 - 22:30

70

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"Two ways" to reduce a module

Published on 07 Sep 2012 - 4:46

243

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Quotient of ring of integers

Published on 10 Oct 2012 - 1:33

List Question

abstract algebra question concerning Euclidean domains

Show that the ring of all rational numbers, which when written in simplest form has an odd denominator, is a principal ideal domain.

If two elements in a ED have the same Euclidean norm, are they associates?

Ring of analytic functions on the circle

Submodule of free module over a p.i.d. is free even when the module is not finitely generated?

Integer extensions, rings $\mathbb{Z}[\sqrt{s}]$

Question about torsion submodules and Decomposition theorem

An integral domain whose every prime ideal is principal is a PID

Every prime ideal is either zero or maximal in a PID.

Exercise on modules over PID involving injective modules, Baer's criterion. (Exercise IV.6.7 in Hungerford's Algebra)

Is $(x^3-x^2+2x-1)$ prime in $\mathbb{Z}/(3)[x]$?

Reference on Operators on Modules over PID

How does a Class group measure the failure of Unique factorization?

"Two ways" to reduce a module

Quotient of ring of integers

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