List questions from integral-domain

Published on 03 Sep 2019 - 11:54

47

Views

Range of functions

Published on 23 Feb 2026 - 8:19

795

Views

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

Published on 05 Sep 2019 - 12:08

350

Views

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

Published on 10 Sep 2019 - 21:15

387

Views

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

Published on 25 Mar 2026 - 7:46

78

Views

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

Published on 16 Sep 2019 - 20:23

208

Views

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

Published on 17 Sep 2019 - 14:45

394

Views

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

Published on 20 Sep 2019 - 13:37

3.3k

Views

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

Published on 16 Mar 2014 - 21:06

909

Views

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

Published on 18 Mar 2014 - 13:51

2.6k

Views

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

Published on 23 Mar 2014 - 13:39

1.4k

Views

Irreducible elements and Associates

Published on 23 Mar 2014 - 20:48

1.5k

Views

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

Published on 24 Mar 2014 - 3:49

193

Views

Properties induced by surjective ring homomorphism between two integral domains

Published on 25 Mar 2014 - 10:43

76

Views

GCD property of Domain

Published on 25 Mar 2014 - 20:59

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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