List questions from principal-ideal-domains

Published on 23 Apr 2014 - 18:53

13.5k

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Irreducible elements in a PID are prime

Published on 27 Apr 2014 - 0:29

133

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Examples of PIDs and prime ideals

Published on 03 May 2014 - 17:06

864

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A submodule of a free module over a PID

Published on 13 May 2014 - 21:24

59

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principal ideals, integral domains, ideals,?

Published on 26 May 2014 - 10:40

36

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Quick question: SES where base ring is a PID

Published on 04 Jun 2014 - 3:35

757

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Show that an integral domain $R$ is principal if and only if every submodule of a cyclic $R$-module is cyclic.

Published on 25 Mar 2026 - 15:53

406

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$M \oplus M \simeq N \oplus N$ then $M \simeq N.$

Published on 21 Jun 2014 - 18:10

123

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Ring Sandwiched between PIDs

Published on 25 Jun 2014 - 7:32

77

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Show that if $R$ is principal, $N $ is pure and $Ann(x+N)= Rd$ then there exists $y \in M$ such that $x+N=y+N$ and $Ann(y)=Rd$

Published on 25 Mar 2026 - 15:55

193

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Intersection of ideals $I=(2x)$ and $J=(2x^2)$ of $\mathbb{Z}[2x,2x^2,2x^3,\dots]$ is not finitely generated.

Published on 25 Mar 2026 - 17:21

244

Views

Smith normal forms and a math program

Published on 28 Jun 2014 - 19:07

29.8k

Views

Ring of integers is a PID but not a Euclidean domain

Published on 25 Mar 2026 - 17:19

3.2k

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Quotient of polynomials, PID but not Euclidean domain?

Published on 11 Jul 2014 - 13:17

27.7k

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In a PID every nonzero prime ideal is maximal

Published on 12 Jul 2014 - 17:56

List Question

Are rank and determinantal rank the same over a PID?

Irreducible elements in a PID are prime

Examples of PIDs and prime ideals

A submodule of a free module over a PID

principal ideals, integral domains, ideals,?

Quick question: SES where base ring is a PID

Show that an integral domain $R$ is principal if and only if every submodule of a cyclic $R$-module is cyclic.

$M \oplus M \simeq N \oplus N$ then $M \simeq N.$

Ring Sandwiched between PIDs

Show that if $R$ is principal, $N $ is pure and $Ann(x+N)= Rd$ then there exists $y \in M$ such that $x+N=y+N$ and $Ann(y)=Rd$

Intersection of ideals $I=(2x)$ and $J=(2x^2)$ of $\mathbb{Z}[2x,2x^2,2x^3,\dots]$ is not finitely generated.

Smith normal forms and a math program

Ring of integers is a PID but not a Euclidean domain

Quotient of polynomials, PID but not Euclidean domain?

In a PID every nonzero prime ideal is maximal

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