List questions from principal-ideal-domains

Published on 29 Mar 2026 - 7:39

261

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Domain of the function $f(x) = \sqrt{\frac{3^x-4^x}{x^2-4x-4}}$ will be?

Published on 04 May 2015 - 6:28

8.1k

Views

Krull dimension of polynomial rings over noetherian rings

Published on 27 Mar 2026 - 16:25

364

Views

Some ring isomorphic to $\mathbb Z[i] / \langle 5 \rangle$

Published on 06 May 2015 - 6:25

265

Views

How we can show that a group algebra over infinite cyclic group is a principal ideal domain?

Published on 25 Mar 2026 - 23:39

101

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subring of a quotient field

Published on 07 May 2015 - 18:31

143

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vector space constructed through a torsion module

Published on 21 May 2015 - 18:30

293

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all abelian groups with 625 elements with 24 elements of order 5

Published on 24 May 2015 - 12:38

106

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Prove that $(5x^3+9x^2-27x+3)$ is a maximal ideal in $\mathbb{Q}[x]$

Published on 26 May 2015 - 10:20

78

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Proving that for an integral domain $R$, $y\in (x)\iff (y)\subseteq (x)$.

Published on 27 Mar 2026 - 6:07

1.7k

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Let $ I $ be an ideal in $\mathbb Z [i]$. Show that $\mathbb Z[i] /I $ is finite.

Published on 26 Mar 2026 - 22:32

836

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Distributive law of ideals in $\mathbf Z$ relating $\cap$ and $+$.

Published on 04 Jun 2015 - 0:44

79

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Principal ideal domain, $\forall x=(x_1,x_2)^t \in R^2~~\exists G \in SL_2(R) : Gx=(\gcd(x_1,x_2), 0)^t$

Published on 16 Jun 2015 - 0:44

8.4k

Views

Proof about finitely generated torsion-free R-module M is free, where R is a PID

Published on 22 Jun 2015 - 12:37

664

Views

Why is $(2,x)$ non-principal in $\Bbb Z[x]$?

Published on 23 Jun 2015 - 1:26

List Question

If in a UFD every maximal ideal is principal then it is a PID

Domain of the function $f(x) = \sqrt{\frac{3^x-4^x}{x^2-4x-4}}$ will be?

Krull dimension of polynomial rings over noetherian rings

Some ring isomorphic to $\mathbb Z[i] / \langle 5 \rangle$

How we can show that a group algebra over infinite cyclic group is a principal ideal domain?

subring of a quotient field

vector space constructed through a torsion module

all abelian groups with 625 elements with 24 elements of order 5

Prove that $(5x^3+9x^2-27x+3)$ is a maximal ideal in $\mathbb{Q}[x]$

Proving that for an integral domain $R$, $y\in (x)\iff (y)\subseteq (x)$.

Let $ I $ be an ideal in $\mathbb Z [i]$. Show that $\mathbb Z[i] /I $ is finite.

Distributive law of ideals in $\mathbf Z$ relating $\cap$ and $+$.

Principal ideal domain, $\forall x=(x_1,x_2)^t \in R^2~~\exists G \in SL_2(R) : Gx=(\gcd(x_1,x_2), 0)^t$

Proof about finitely generated torsion-free R-module M is free, where R is a PID

Why is $(2,x)$ non-principal in $\Bbb Z[x]$?

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