List questions from principal-ideal-domains

Published on 13 Dec 2018 - 15:22

742

Views

If $R$ is a principal ideal domain and $s$ is a non-zero prime ideal, then $\frac{R}{s}$ has finitely many prime ideals .

Published on 14 Dec 2018 - 7:01

187

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Counterexample PID

Published on 25 Mar 2026 - 12:12

110

Views

Step in proof of Structure Theorem for finitely generated modules over a PID

Published on 04 Jan 2019 - 0:52

1.4k

Views

Gaussian Integers form an Euclidean Ring

Published on 26 Mar 2026 - 11:07

152

Views

Showing that an ideal is not principal in $\mathbb{Z}[\sqrt{-21}]$

Published on 08 Jan 2019 - 20:04

146

Views

Showing that an ideal in $\mathbb{Z}[\sqrt{-21}]$ is principal

Published on 09 Jan 2019 - 16:18

759

Views

When is a Unique Factorization Domain a Principal Ideal domain

Published on 25 Mar 2026 - 6:00

243

Views

Integral Domain, PID and gcd

Published on 25 Mar 2026 - 5:59

301

Views

Is the ideal generated by ${4,x}$ a principal ideal in $Z[x]$?

Published on 12 Jan 2019 - 15:46

58

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Prove that for $\pi_g(\alpha)=\alpha g$, $\pi$ is a group action

Published on 26 Mar 2026 - 12:35

63

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Determine the quotient and the remainder of the division:

Published on 25 Mar 2026 - 15:43

327

Views

Let $ R $ be a p.i.d. and $ A\in M_n(R) $. If $ \det(A)=1 $, prove or disprove that $ A $ can be expressed as products of elementary matrices.

Published on 23 Jan 2019 - 13:12

438

Views

Is every ideal of Quotient Ring a PID?

Published on 23 Jan 2019 - 16:26

164

Views

$I$ an irreducible ideal in a PID is a prime ideal

Published on 24 Jan 2019 - 18:08

List Question

$R=\{f(x)\in \mathbb{Q}[x] | f'(0)=0 \}$ is not PID

If $R$ is a principal ideal domain and $s$ is a non-zero prime ideal, then $\frac{R}{s}$ has finitely many prime ideals .

Counterexample PID

Step in proof of Structure Theorem for finitely generated modules over a PID

Gaussian Integers form an Euclidean Ring

Showing that an ideal is not principal in $\mathbb{Z}[\sqrt{-21}]$

Showing that an ideal in $\mathbb{Z}[\sqrt{-21}]$ is principal

When is a Unique Factorization Domain a Principal Ideal domain

Integral Domain, PID and gcd

Is the ideal generated by ${4,x}$ a principal ideal in $Z[x]$?

Prove that for $\pi_g(\alpha)=\alpha g$, $\pi$ is a group action

Determine the quotient and the remainder of the division:

Let $ R $ be a p.i.d. and $ A\in M_n(R) $. If $ \det(A)=1 $, prove or disprove that $ A $ can be expressed as products of elementary matrices.

Is every ideal of Quotient Ring a PID?

$I$ an irreducible ideal in a PID is a prime ideal

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