List questions from principal-ideal-domains

Published on 25 Mar 2026 - 22:06

608

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module over a quotient of a principal ideal domain

Published on 28 Jul 2014 - 10:49

2.2k

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Is $\mathbb{C}[x,y] / (y^2-x^3)$ a PID?

Published on 28 Jul 2014 - 12:15

494

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Corollary to Smith normal form

Published on 29 Jul 2014 - 12:01

74

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Is the ideal $(2,x^4+x^2+1)<\mathbb{Z}[x]$ maximal?, principal?

Published on 06 Aug 2014 - 8:34

124

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Help understanding statement relating to structure of modules over PIDs

Published on 14 Aug 2014 - 2:02

1k

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Difference between PID and principal ideal ring

Published on 10 Sep 2014 - 15:33

16.4k

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Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.

Published on 21 Sep 2014 - 17:20

92

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The number 2 in a PID

Published on 26 Mar 2026 - 20:50

96

Views

Principal Ideal Domain Modulo a Power of a Prime Ideal

Published on 27 Sep 2014 - 23:33

134

Views

algebraic poset

Published on 29 Sep 2014 - 16:50

690

Views

Problem with Smith normal form over a PID that is not an Euclidean domain

Published on 23 Feb 2026 - 6:05

461

Views

$\Bbb Z[x]$ is not a principal domain

Published on 07 Oct 2014 - 11:48

260

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Principal Ideal Domains with Many Primes of Index 2

Published on 10 Oct 2014 - 4:07

407

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Suppose that $K$ is a field and that $f$ and $g$ are relatively prime in $K[x]$. Show that $f - Yg$ is irreducible in $K(y)[x]$.

Published on 13 Oct 2014 - 20:46

List Question

R is a PID, and a is a nonzero nonunit in R. How can we show R/Ra is an injective module over R?

module over a quotient of a principal ideal domain

Is $\mathbb{C}[x,y] / (y^2-x^3)$ a PID?

Corollary to Smith normal form

Is the ideal $(2,x^4+x^2+1)<\mathbb{Z}[x]$ maximal?, principal?

Help understanding statement relating to structure of modules over PIDs

Difference between PID and principal ideal ring

Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.

The number 2 in a PID

Principal Ideal Domain Modulo a Power of a Prime Ideal

algebraic poset

Problem with Smith normal form over a PID that is not an Euclidean domain

$\Bbb Z[x]$ is not a principal domain

Principal Ideal Domains with Many Primes of Index 2

Suppose that $K$ is a field and that $f$ and $g$ are relatively prime in $K[x]$. Show that $f - Yg$ is irreducible in $K(y)[x]$.

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