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Do these facts about $\mathbb{Q}/\mathbb{Z}$ generalize to more general cases?

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#abstract-algebra #modules #injective-module
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Analogue of Baer criterion for testing projectiveness of modules

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#abstract-algebra #modules #projective-module #injective-module
288
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Localization of Gorenstein ring

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#commutative-algebra #homological-algebra #injective-module #gorenstein
353
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Injective resolution for an integral domain

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#commutative-algebra #noncommutative-algebra #projective-module #injective-module
372
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Injective modules in a short exact sequence

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#commutative-algebra #projective-module #injective-module
241
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Comparing injective dimensions in a short exact sequence

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#ring-theory #commutative-algebra #homological-algebra #injective-module
182
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Finite projective dimension may lead to projectiveness!

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1.8k
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Injective dimension of $\mathbb Z_n$ as a $\mathbb Z$-module

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#commutative-algebra #homological-algebra #injective-module
752
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Examples of Noetherian local rings which are not Gorenstein

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#commutative-algebra #homological-algebra #noetherian #injective-module #gorenstein
199
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$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective

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Integral domain with a finitely generated non-zero injective module is a field

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#abstract-algebra #ring-theory #commutative-algebra #modules #injective-module
738
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What is the injective envelope of $\mathbb{Z}/n\mathbb{Z}$?

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#abstract-algebra #homological-algebra #injective-module
1k
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Projective modules over $kG$ equivalent to injective.

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#abstract-algebra #homological-algebra #projective-module #injective-module #group-rings
82
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R is a PID, and a is a nonzero nonunit in R. How can we show R/Ra is an injective module over R?

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#abstract-algebra #principal-ideal-domains #injective-module
198
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$\Gamma_{\mathfrak a}(I)$ is an injective $R$-module for every injective $R$-module $I$

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#commutative-algebra #injective-module #local-cohomology

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