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15
54
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Subcategory determined by composition series

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#abstract-algebra #category-theory #modules
121
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A finite abelian group $A$ can not be a projective $\mathbb{Z}$-module.

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#abstract-algebra #modules #abelian-groups #projective-module
109
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Show that if $Q$ is a non-trivial $\mathbb{Z}$-module, that is divisible, then $Q$ can not be a projective $\mathbb{Z}$-module.

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#modules #projective-module #free-modules
73
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Projective-injective modules over $k[x]$

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#abstract-algebra #modules #homological-algebra #graded-rings
84
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$R$-module structure of tensor product of $R$-algebras (Atiyah-Macdonald)

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#commutative-algebra #modules #tensor-products
24
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Exact sequence is such that it lifts for every homomorphism to another R-module, then it lifts to $\operatorname{Hom}_{\mathbb{Z}}(R,M)$

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#modules #exact-sequence
44
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Is there always a free $\mathbb{Q}$-module on a set $A$?

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#modules
87
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Pushout of $R$-modules.

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#abstract-algebra #modules
46
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How to write a principal ideal as $R$-module?

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#abstract-algebra #modules
38
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Question about when the restriction of a tensor-product to a submodule in one of its arguments agrees with the unrestricted tensor-product on element

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#modules #tensor-products
56
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Dedekind domain, non PID, localization over maximal ideals.

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#abstract-algebra #ring-theory #modules #localization #dedekind-domain
177
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Is $N_1+N_2\cong N_1\oplus N_2$ iff $N_1\cap N_2=(0)$?

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#abstract-algebra #ring-theory #commutative-algebra #modules #finitely-generated
67
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Isomorphism of projective modules modulo nilpotent ideals.

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#commutative-algebra #modules #projective-module #algebraic-k-theory
50
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How are eigenspaces of an vector space endomorphism related to the decomposition as a direct sum of abelian groups?

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#abstract-algebra #category-theory #modules #abelian-groups #minimal-polynomials
31
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Module written as direct sum

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#abstract-algebra #ring-theory #modules #noncommutative-algebra #direct-sum

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