List questions from commutative-algebra

Published on 27 Mar 2026 - 5:37

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local (not Noetherian) domain satisfying a.c.c. on radical ideals and satisfying d.c.c on prime ideals

Published on 27 Mar 2026 - 13:47

269

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How to show $\operatorname{Hom}_A(M,N)$ is a finitely generated $A$-module?

Published on 28 Mar 2026 - 20:07

80

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In a commutative ring $R$ if, for every $a\in R$, the smallest ideal containing $a$ is equal to $Ra$ then $R$ has identity?

Published on 03 Apr 2026 - 9:23

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A lemma of Krull Intersection Theorem.

Published on 04 Oct 2018 - 9:08

750

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GCD in arbitrary domain

Published on 25 Mar 2026 - 12:13

178

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$M/PM$ is torsion-free

Published on 31 Mar 2026 - 18:28

48

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Find example of nonhomogeneous ideal in $\mathbb{k}[x]$ which has two different minimal generating sets are not equipotent.

Published on 29 Mar 2026 - 13:29

78

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Diophantine Equations over polynomial rings

Published on 27 Mar 2026 - 2:50

227

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Sheaf of Differentials on a product

Published on 04 Oct 2018 - 16:49

1.2k

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Flat ring homomorphism but not injective.

Published on 04 Oct 2018 - 17:54

44

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Two definitions of a local property of rings and modules.

Published on 25 Mar 2026 - 23:38

54

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Radicals and Ideals

Published on 29 Mar 2026 - 13:21

78

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Is there a nonzero module $M$ over an artinian local ring $(R,\mathfrak m)$ such that $\mathfrak mM=M\ ?$

Published on 25 Mar 2026 - 1:16

171

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Can you determine the transcendence degree of an algebra by looking at a generating set?

Published on 01 Apr 2026 - 3:02

List Question

Counting Homogeneous Forms on Elliptic Curves

local (not Noetherian) domain satisfying a.c.c. on radical ideals and satisfying d.c.c on prime ideals

How to show $\operatorname{Hom}_A(M,N)$ is a finitely generated $A$-module?

In a commutative ring $R$ if, for every $a\in R$, the smallest ideal containing $a$ is equal to $Ra$ then $R$ has identity?

A lemma of Krull Intersection Theorem.

GCD in arbitrary domain

$M/PM$ is torsion-free

Find example of nonhomogeneous ideal in $\mathbb{k}[x]$ which has two different minimal generating sets are not equipotent.

Diophantine Equations over polynomial rings

Sheaf of Differentials on a product

Flat ring homomorphism but not injective.

Two definitions of a local property of rings and modules.

Radicals and Ideals

Is there a nonzero module $M$ over an artinian local ring $(R,\mathfrak m)$ such that $\mathfrak mM=M\ ?$

Can you determine the transcendence degree of an algebra by looking at a generating set?

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