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How Should I Prove this Function is Well-defined?

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#abstract-algebra #ring-theory #modules #projective-module #injective-module
68
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If a Short Exact Sequence is Split-Exact, Does that Mean it is Left-Split?

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#abstract-algebra #modules #projective-module #injective-module
62
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Is Every Isomorphism on Tensor Product of Modules an R-module Isomorphism?

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#abstract-algebra #modules #localization #projective-module #flatness
42
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How Can We Prove Flatness from an Induced Exact Sequence?

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#abstract-algebra #modules #projective-module #flatness #injective-module
117
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Are projective modules free over a polynomial ring with infinite indeterminates over a field?

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#polynomials #projective-module #free-modules
33
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partial Quillen-Suslin on square matrix

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#abstract-algebra #algebraic-geometry #projective-module #free-modules
19
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Is every projective R-module torsion-free? when R is a noncommutative ring!

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#noncommutative-algebra #projective-module
20
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Are injective maps of finite modules over regular ring liftable to termwise injective maps of finite projective resolution?

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#homological-algebra #projective-module #regular-rings
90
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Tensor product of projective modules.

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#abstract-algebra #commutative-algebra #modules #tensor-products #projective-module
122
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$M_1 \oplus M_2$ is projective $\iff M_1$ and $M_2$ are both projective

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#category-theory #modules #homological-algebra #projective-module
49
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Incorrect proof for $e$ idempotent $\Rightarrow$ $eA$ projective

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#abstract-algebra #modules #fake-proofs #projective-module #idempotents
116
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Why a nonzero finite abelian group is not projective?

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#abstract-algebra #modules #exact-sequence #projective-module #free-modules
62
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Projective module over a commutative ring $R$ becomes free over some ring containing $R$ .

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#number-theory #ring-theory #modules #projective-module
112
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How Should I Prove that M is Torsion-free Given that M is Projective?

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#abstract-algebra #ring-theory #modules #projective-module
97
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If $M$ is a finitely generated module over a local ring, then $M$ is free.

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#abstract-algebra #commutative-algebra #modules #localization #projective-module

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