List questions from principal-ideal-domains

Published on 08 Mar 2022 - 20:10

40

Views

Basis for Module Over PID

Published on 29 Mar 2026 - 22:44

119

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Why are the direct summands obtained in the structure theorem for finitely generated modules over a PID indecomposable?

Published on 30 Mar 2026 - 12:31

90

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What does the correspondence theorem tell us about the ideals of $\Bbb Z[x]$ that contain $x^2+1$?

Published on 25 Mar 2022 - 16:22

139

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Question on Definition of Canonical Epimorphism

Published on 12 May 2022 - 0:05

315

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On Showing that $\mathbb{Z}[x]$ is not a Principal Ideal Domain

Published on 12 May 2022 - 19:46

21

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How can I finish the proof for the following proposition: every ideal in k[x] is a principal ideal?

Published on 19 May 2022 - 14:20

417

Views

Bezout Lemma in a PID

Published on 23 May 2022 - 11:25

69

Views

Quotient, regular modules and submodules PID.

Published on 24 May 2022 - 23:07

62

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Localization of the ring of Laurent polynomial

Published on 01 Apr 2026 - 12:06

214

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Is the ring of formal power series $\mathbb K[[x_1, \dots, X_n]]$ in $n$ indeterminates over a field a PID?

Published on 27 Mar 2026 - 11:48

133

Views

How to obtain generator of principal ideal

Published on 04 Jun 2022 - 12:27

88

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If a ring is not an integral domain does it then implies that it is not a PID?

Published on 08 Jun 2022 - 9:06

41

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Is it true that an uniformizing element of a discrete valuation ring $R$ is either zero or prime?

Published on 31 Mar 2026 - 3:45

51

Views

Let $R$ be a PID and $a \in R$ is non-invertible,then $\exists$ some prime element $p$ such that $p|a.$

Published on 29 Jun 2022 - 11:13

List Question

Principal ideal domain - polynomial ring

Basis for Module Over PID

Why are the direct summands obtained in the structure theorem for finitely generated modules over a PID indecomposable?

What does the correspondence theorem tell us about the ideals of $\Bbb Z[x]$ that contain $x^2+1$?

Question on Definition of Canonical Epimorphism

On Showing that $\mathbb{Z}[x]$ is not a Principal Ideal Domain

How can I finish the proof for the following proposition: every ideal in k[x] is a principal ideal?

Bezout Lemma in a PID

Quotient, regular modules and submodules PID.

Localization of the ring of Laurent polynomial

Is the ring of formal power series $\mathbb K[[x_1, \dots, X_n]]$ in $n$ indeterminates over a field a PID?

How to obtain generator of principal ideal

If a ring is not an integral domain does it then implies that it is not a PID?

Is it true that an uniformizing element of a discrete valuation ring $R$ is either zero or prime?

Let $R$ be a PID and $a \in R$ is non-invertible,then $\exists$ some prime element $p$ such that $p|a.$

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