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15
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Conditions on a Module Implied by $\mathrm{Ext}^1 = 0$

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#abstract-algebra #modules #homological-algebra #exact-sequence #projective-module
1k
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Inner product in module theory

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#ring-theory #commutative-algebra #modules #inner-products #projective-module
1.6k
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Prove that no $\mathbb{Z}$-module is both projective and injective

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#projective-module #injective-module
183
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If $R$ is a Dedekind domain and $I, J \triangleleft R$, then $R^d \oplus I \simeq R^{d'} \oplus J$ implies $d = d'$ and $I \simeq J$

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#abstract-algebra #modules #projective-module #dedekind-domain
198
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projective resolution of bimodules

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#homological-algebra #projective-module
113
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Grassmannian as a functor and the rank of a projective module.

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#algebraic-geometry #commutative-algebra #modules #projective-module #free-modules
662
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Projective Resolution of $C[x,y,t]/(x^2+y^2-t)$

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#algebraic-geometry #homological-algebra #exact-sequence #projective-module #free-modules
1k
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Projective and flat vs. faithfully flat

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#commutative-algebra #modules #tensor-products #projective-module #flatness
77
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When limits preserve projectivity

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#abstract-algebra #ring-theory #projective-module
418
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Are these two definitions stably isomorphic modules / $K_0(A)$ equivalent?

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#projective-module #algebraic-k-theory
196
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Categorical Kernel is Module Kernel

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#category-theory #projective-module #finitely-generated
825
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Enough injectives in the category of chain complexes

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#category-theory #homological-algebra #abelian-categories #projective-module #injective-module
312
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Radical of projective modules

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#commutative-algebra #projective-module
247
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Prove that $A \otimes_{\mathrm{R}} B$ is a projective $\mathbb{Z}$- module.

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#tensor-products #projective-module
428
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P is a projective module. Prove that there exists $F$ free such that $P \oplus F \cong F$

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#homological-algebra #projective-module #free-modules

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