List questions from principal-ideal-domains

Published on 12 Aug 2013 - 14:42

1.2k

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On a PID that is not an Euclidean domain

Published on 26 Mar 2026 - 22:36

2.8k

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number of element in a principal ideal domain can be $25/36/35/15$?

Published on 18 Aug 2013 - 12:00

216

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Counting the ideals of $\frac{\mathbb{R}[X]}{(X^2)}$

Published on 27 Aug 2013 - 13:48

242

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PID modulo a non-zero ideal is a semilocal ring

Published on 04 Sep 2013 - 14:10

340

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Number of ideals in $\Bbb Z[x]/(x^3+1, 7)$

Published on 10 Sep 2013 - 7:29

44.9k

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Is $\mathbb{Z}[x]$ a principal ideal domain?

Published on 21 Sep 2013 - 10:56

1k

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Confusion regarding the proof of "Every PID satisfies the Ascending Chain Condition".

Published on 18 Oct 2013 - 6:55

1.8k

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Integral domain in complex numbers.

Published on 28 Mar 2026 - 3:00

9.1k

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Is the quotient ring of a PID a PID?

Published on 30 Mar 2026 - 7:39

174

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In the proof that in a PID, every non-zero non-unit is the product of irreducibles...

Published on 27 Oct 2013 - 18:38

84

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Understanding this basic lemma proof in Ireland & Rosen

Published on 28 Oct 2013 - 18:29

8.1k

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Proving that a ring is not a Principal Ideal Domain

Published on 28 Mar 2026 - 3:02

76

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Inclusion-minimality of a lattice basis

Published on 28 Mar 2026 - 7:32

1.6k

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surjective homomorphism between principal ideal rings

Published on 23 Feb 2026 - 4:38

List Question

Principal Ideal Domain Basics.

On a PID that is not an Euclidean domain

number of element in a principal ideal domain can be $25/36/35/15$?

Counting the ideals of $\frac{\mathbb{R}[X]}{(X^2)}$

PID modulo a non-zero ideal is a semilocal ring

Number of ideals in $\Bbb Z[x]/(x^3+1, 7)$

Is $\mathbb{Z}[x]$ a principal ideal domain?

Confusion regarding the proof of "Every PID satisfies the Ascending Chain Condition".

Integral domain in complex numbers.

Is the quotient ring of a PID a PID?

In the proof that in a PID, every non-zero non-unit is the product of irreducibles...

Understanding this basic lemma proof in Ireland & Rosen

Proving that a ring is not a Principal Ideal Domain

Inclusion-minimality of a lattice basis

surjective homomorphism between principal ideal rings

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