List questions from principal-ideal-domains

34

Views

Question about a step in the proof of the uniqueness of the decomposition of a finitely generated R-module, R a PID.

Published on 27 Mar 2026 - 14:03

301

Views

Applying the elementary divisor theorem

Published on 26 Mar 2026 - 12:51

63

Views

If $a+bc$ and $c$ have irreducible factors in common, then $a$ and $c$ have the same irreducible factors in common.

Published on 25 May 2020 - 13:58

293

Views

Finding all the maximal ideals of $\mathbb{Z}_{63}$

Published on 26 May 2020 - 22:55

139

Views

Proof of $A\left [ \left [ x \right ] \right ]$ PID implies $A$ is a field

Published on 26 Mar 2026 - 8:14

124

Views

Ascending chain of ideal in polynomial ring

Published on 02 Jun 2020 - 15:37

58

Views

A problem regarding polynomials with only prime powers

Published on 02 Jun 2020 - 20:42

152

Views

A module over PID

Published on 27 Mar 2026 - 23:46

353

Views

Length of a module over a PID

Published on 04 Jun 2020 - 20:57

398

Views

Every proper ideal can be written as a product of maximal ideals in PID (product and intersection)

Published on 26 Mar 2026 - 0:53

332

Views

Does irreducibility corresponds to maximal ideals.

Published on 26 Mar 2026 - 2:34

94

Views

Ideals of the ring $\mathbb{Z}_3[x]/\langle x^4+x^3+x+1\rangle$

Published on 13 Jun 2020 - 8:09

1.5k

Views

How to prove Gaussian Integers is a UFD Formally

Published on 26 Mar 2026 - 0:52

717

Views

When is $\mathbb Z[\sqrt d]$ a Euclidean or principal ideal domain?

Published on 26 Mar 2026 - 4:31

71

Views

Integral domains and principal ideals

Published on 28 Jun 2020 - 0:51

List Question

Question about a step in the proof of the uniqueness of the decomposition of a finitely generated R-module, R a PID.

Applying the elementary divisor theorem

If $a+bc$ and $c$ have irreducible factors in common, then $a$ and $c$ have the same irreducible factors in common.

Finding all the maximal ideals of $\mathbb{Z}_{63}$

Proof of $A\left [ \left [ x \right ] \right ]$ PID implies $A$ is a field

Ascending chain of ideal in polynomial ring

A problem regarding polynomials with only prime powers

A module over PID

Length of a module over a PID

Every proper ideal can be written as a product of maximal ideals in PID (product and intersection)

Does irreducibility corresponds to maximal ideals.

Ideals of the ring $\mathbb{Z}_3[x]/\langle x^4+x^3+x+1\rangle$

How to prove Gaussian Integers is a UFD Formally

When is $\mathbb Z[\sqrt d]$ a Euclidean or principal ideal domain?

Integral domains and principal ideals

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