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$M$ finitely generated over $(R,\mathfrak{m})\Rightarrow M/\mathfrak{m}M$ artinian

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#commutative-algebra #artinian
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Primary ideals in an Artinial local ring

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#ring-theory #commutative-algebra #artinian
48
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Primary decomposition in a finite algebra

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#abstract-algebra #ring-theory #commutative-algebra #maximal-and-prime-ideals #artinian
74
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Projectivity of a module

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#abstract-algebra #modules #projective-module #artinian
544
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Maximal and prime ideal in an artinian ring

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#maximal-and-prime-ideals #artinian
234
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Example of a module that is finitely generated, finitely cogenerated and linearly compact, but not Artinian!

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#abstract-algebra #commutative-algebra #finitely-generated #artinian
478
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If M is a a left module over $M_n(D)$ where $D$ is a division ring, M is Noetherian iff Artinian

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#abstract-algebra #ring-theory #modules #noetherian #artinian
195
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Checking if quotient ring is Noetherian or Artinian over a module

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#commutative-algebra #modules #noetherian #artinian
308
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Infinite Artin ring with only finitely many units

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#abstract-algebra #ring-theory #commutative-algebra #artinian
385
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Question about Hopkins-Levitzki Theorem's proof

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#modules #noetherian #artinian #semi-simple-rings
395
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Jacobson local ring that is not Artinian

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#commutative-algebra #noetherian #artinian
62
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Artinian local ring with every non-maximal ideal being principal

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#commutative-algebra #ideals #local-rings #artinian
147
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Artinian algebra over algebraicly closed field

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#abstract-algebra #artinian
68
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$R$ is artinian $\implies$ $(eR)_R$ is local $R$-module for an idempotent $e \in R$

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#modules #idempotents #local-rings #artinian
1k
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Is a local ring Artinian, if the maximal ideal is nilpotent?

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#abstract-algebra #commutative-algebra #artinian

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