List questions from integral-domain

Published on 10 May 2026 - 14:59

52

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Range of functions

Published on 14 Apr 2026 - 19:47

798

Views

$\mathbb{Z}[\sqrt{-7}]$ is not an Euclidian Domain

Published on 11 Apr 2026 - 15:00

353

Views

The ideal which is not principal in $\Bbb Z[i\sqrt{6}]$

Published on 10 Apr 2026 - 7:52

389

Views

Primary decomposition of the zero submodule of a module $M$, and of the annihilator of $M$

Published on 10 May 2026 - 20:44

81

Views

$p\in\operatorname{Ass}(M)\iff \exists$ injective $R/p\to M$

Published on 16 Apr 2026 - 20:43

211

Views

Can an indecomposable module be neither torsion nor torsion-free?

Published on 11 Apr 2026 - 19:30

397

Views

Show that $R\cong Rx$ (as rings) if and only if $x$ is an unit.

Published on 15 Apr 2026 - 19:29

3.3k

Views

In a noetherian integral domain every non invertible element is a product of irreducible elements

Published on 16 Apr 2026 - 11:56

912

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What is the normalization of the ring $\mathbb C[x,y,t]/(t^3-x^3y)$?

Published on 16 Apr 2026 - 16:41

2.6k

Views

Why $\Bbb Z$ = (integers) is an integral domain?

Published on 09 Apr 2026 - 17:14

1.4k

Views

Irreducible elements and Associates

Published on 14 Apr 2026 - 23:24

1.5k

Views

Every submodule of free $R$-module is free; is $R$ an integral domain?

Published on 12 Apr 2026 - 9:59

196

Views

Properties induced by surjective ring homomorphism between two integral domains

Published on 12 Apr 2026 - 9:56

80

Views

GCD property of Domain

Published on 10 May 2026 - 20:27

List Question

$\mathbb{Z}[\sqrt{2}]$ is a euclidean domain

Range of functions

$\mathbb{Z}[\sqrt{-7}]$ is not an Euclidian Domain

The ideal which is not principal in $\Bbb Z[i\sqrt{6}]$

Primary decomposition of the zero submodule of a module $M$, and of the annihilator of $M$

$p\in\operatorname{Ass}(M)\iff \exists$ injective $R/p\to M$

Can an indecomposable module be neither torsion nor torsion-free?

Show that $R\cong Rx$ (as rings) if and only if $x$ is an unit.

In a noetherian integral domain every non invertible element is a product of irreducible elements

What is the normalization of the ring $\mathbb C[x,y,t]/(t^3-x^3y)$?

Why $\Bbb Z$ = (integers) is an integral domain?

Irreducible elements and Associates

Every submodule of free $R$-module is free; is $R$ an integral domain?

Properties induced by surjective ring homomorphism between two integral domains

GCD property of Domain

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