List questions from artinian

Published on 25 Mar 2026 - 4:38

162

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Is a complete intersection ring, which is a quotient of a maximal $A$-sequence, Artinian?

Published on 19 Mar 2026 - 20:06

512

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"categorical" proof of a seemingly symmetric statement about Noetherian/Artinian modules

Published on 25 Mar 2026 - 4:40

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

36

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On a special type of ideal in local Artinian ring

Published on 25 Mar 2026 - 3:02

62

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Is this ring Noetherian? Artinian?

Published on 22 Mar 2026 - 9:30

195

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Divided power algebra is artinian as a module over the polynomial ring

Published on 25 Mar 2026 - 3:00

275

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How could I construct a module $M$ that has exactly $n$ composition series?

Published on 20 Nov 2018 - 17:20

251

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A completely reducible module is Artinian if and only if it is Noetherian.

Published on 23 Nov 2018 - 10:14

230

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Commutative local ring with $10$ ideals

Published on 25 Mar 2026 - 2:57

719

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For an Artinian ring semiprimitive implies semisimple.

Published on 23 Feb 2026 - 0:24

163

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$\mathbb{R} ^ \mathbb{R}$ is a commutative ring with identity that is neither noetherian nor artinian.

Published on 08 Jan 2019 - 8:07

206

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The Kernel is inside the radical when we have an essential epimorphism

Published on 14 Jan 2019 - 21:16

463

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Algebras finite-dimensional over their base field are Artinian.

Published on 23 Jan 2019 - 0:18

181

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Does the category of artinian rings admit finite limits?

Published on 25 Mar 2026 - 4:40

List Question

Show that this Artinian ring is also Noetherian.

Is a complete intersection ring, which is a quotient of a maximal $A$-sequence, Artinian?

"categorical" proof of a seemingly symmetric statement about Noetherian/Artinian modules

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

On a special type of ideal in local Artinian ring

Is this ring Noetherian? Artinian?

Divided power algebra is artinian as a module over the polynomial ring

How could I construct a module $M$ that has exactly $n$ composition series?

A completely reducible module is Artinian if and only if it is Noetherian.

Commutative local ring with $10$ ideals

For an Artinian ring semiprimitive implies semisimple.

$\mathbb{R} ^ \mathbb{R}$ is a commutative ring with identity that is neither noetherian nor artinian.

The Kernel is inside the radical when we have an essential epimorphism

Algebras finite-dimensional over their base field are Artinian.

Does the category of artinian rings admit finite limits?

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