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Simple tensors and projective modules

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#abstract-algebra #ring-theory #representation-theory #homological-algebra #projective-module
64
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If $f:R\to S$ is an $R$-algebra and $P$ is a projective $S$-module, then $pd_R(P)\le pd_R(S)$.

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#homological-algebra #projective-module
152
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Proof of Quillen's patching theorem

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#commutative-algebra #modules #projective-module
87
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$K$-group of category of bounded chain complexes of free modules with finite length homologies

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#commutative-algebra #homological-algebra #projective-module #algebraic-k-theory #additive-categories
420
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R is projective Q-module?

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#projective-module
144
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The duality on projective modules takes minimal presentations to minimal presentations

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#representation-theory #projective-module #algebras
304
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Are projective modules over $\mathbb{Z}[x_1,...,x_m]$ free?

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#abstract-algebra #ring-theory #commutative-algebra #projective-module #free-modules
426
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Projective graded modules

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#commutative-algebra #modules #homological-algebra #projective-module #graded-rings
99
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Why is a projective module called "projective"?

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#abstract-algebra #homological-algebra #projective-module #map-projections
121
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Isomorphic for free modules implies for projective

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#commutative-algebra #modules #projective-module
121
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Question on projective modules, a course in homological algebra

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#abstract-algebra #proof-verification #commutative-algebra #modules #projective-module
2k
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$Q$ is an injective module iff injections from $Q$ always split

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#abstract-algebra #proof-verification #homological-algebra #projective-module #injective-module
430
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Verma flag (or standard filtration) on a direct summand.

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#modules #representation-theory #projective-module #free-modules #verma-modules
108
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An equivalent formulation of the definition of a projective module

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#abstract-algebra #ring-theory #modules #homological-algebra #projective-module
115
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Sum of a faithfully flat module and a flat module

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#modules #homological-algebra #projective-module #flatness

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