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Global dimension of $\mathbb Q [x]$

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#ring-theory #commutative-algebra #modules #homological-algebra #projective-module
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Why $\mathbb{Q}$ is not a projective $\mathbb{Z}$-module?

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#abstract-algebra #modules #projective-module
139
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If a left ideal of R is a direct summand of R, is I an injective R-module?

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#homological-algebra #projective-module #injective-module
115
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If a left ideal I of R is an injective R-module then I is a projective R-module. Is the converse true?

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#homological-algebra #projective-module #injective-module
518
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Is there an analogue of Bass-Papp theorem for Projective modules?

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#abstract-algebra #ring-theory #modules #projective-module #injective-module
511
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The existence of a projective resolution of M from finite rank free modules

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#abstract-algebra #modules #projective-module #noetherian
1.1k
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Why is $(X,Y)$ not a projective $\mathbb{Z}[X,Y]$-module?

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#abstract-algebra #projective-module
348
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Analogue of Baer criterion for testing projectiveness of modules

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#abstract-algebra #modules #projective-module #injective-module
181
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Finite projective resolution of vector spaces

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#abstract-algebra #projective-module
97
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The meaning of functor $M \mapsto \mbox{Hom}_A(P,M)$ being exact

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#abstract-algebra #modules #projective-module
236
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If $R$ is a noetherian local ring, then every 2-generated ideal has finite projective dimension iff $R$ is a UFD

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#ring-theory #commutative-algebra #homological-algebra #projective-module #unique-factorization-domains
354
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Injective resolution for an integral domain

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#commutative-algebra #noncommutative-algebra #projective-module #injective-module
373
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Injective modules in a short exact sequence

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#commutative-algebra #projective-module #injective-module
183
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Finite projective dimension may lead to projectiveness!

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#commutative-algebra #homological-algebra #projective-module #injective-module
197
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Cover of a direct summand

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#modules #projective-module

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