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Given a projective $R$-module $M$, how does one find another $R$-module $N$ such that $M \oplus N$ is a free $R$-module?

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#abstract-algebra #ring-theory #commutative-algebra #modules #projective-module
40
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Rigidity of finitely generated projective modules

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#modules #projective-module #morita-equivalence
64
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If $P$ is projective, then $Ext(P,\_)=0$

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#solution-verification #homological-algebra #projective-module
40
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If $Ext(P,\_) = 0,$ then $P$ is projective

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#homological-algebra #projective-module
32
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Let $R$ be a ring $P$ a projective generator of right $R$-modules. If $M$ is a left $A$-module, then $M \cong \text{Hom}_R(P, P \otimes_R M)$

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#modules #tensor-products #projective-module #morita-equivalence
24
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Clarification about stable module category

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#category-theory #modules #projective-module
548
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A free direct sum of a projective module

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#abstract-algebra #modules #noncommutative-algebra #projective-module
144
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Bass' paper on Gorenstein rings

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#commutative-algebra #projective-module #proof-explanation #gorenstein
172
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Projective modules over enveloping algebra

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#abstract-algebra #noncommutative-algebra #projective-module
54
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Projectivity of a certain module

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#abstract-algebra #modules #noncommutative-algebra #projective-module
1.9k
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Hartshorne II Ex 5.9(a) or R. Vakil Ex 15.4.D(b): Saturated modules

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#algebraic-geometry #modules #projective-module #quasicoherent-sheaves
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Characterization of projective and injective modules

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#modules #projective-module #injective-module
1.3k
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Semisimplicity is equivalent to each simple left module is projective?

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#abstract-algebra #ring-theory #noncommutative-algebra #projective-module
514
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Projective dimension of module over local ring

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#abstract-algebra #ring-theory #commutative-algebra #homological-algebra #projective-module
850
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Equivalent properties of projective modules

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#abstract-algebra #modules #projective-module

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