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Do we have $\oplus_{i=1}^d M_i\cong \sum_{i=1}^d M_i$?

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#abstract-algebra #modules
139
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tensor product of a right and a left D-module

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#abstract-algebra #modules #tensor-products
1.1k
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Pure submodule is a direct summand of a module

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#abstract-algebra #modules #direct-sum
36
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A noetherian $R$-module $M$ with submodules $L,N$ s.t $L\cap N={0}$ and $M/N\cong L$

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#abstract-algebra #modules #examples-counterexamples #noetherian
304
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Modules and set of finite linear combinations

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#abstract-algebra #vector-spaces #modules #definition
439
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Definition of tensor product for modules

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#linear-algebra #vector-spaces #modules #definition #tensor-products
62
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Isomorphism of $S[t^2]$-modules

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#abstract-algebra #ring-theory #modules #graded-rings
77
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Show that $0\cdot m = 0$

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#abstract-algebra #modules
314
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Difference between $\mathbb{Z}_2 \oplus \mathbb{Z}_2$ and $\mathbb{Z}_2 + \mathbb{Z}_2$

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#abstract-algebra #modules
33
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Hopfian module over commutative ring

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#abstract-algebra #commutative-algebra #modules
1.2k
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If $F_1$ and $F_2$ are free modules on the same set $A$, then $F_1 \cong F_2$

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#abstract-algebra #modules #free-modules
609
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Endomorphism of finite dimensional vector space composes to give equal kernels and images

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#linear-algebra #abstract-algebra #ring-theory #vector-spaces #modules
610
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If an abelian group $A$ is injective as $\mathbb{Z}$ module then $A$ is a divisible group

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#category-theory #modules #abelian-groups #injective-module #divisible-groups
634
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What is the meaning of 'Lattices in $\mathbb R^2$ are free $\mathbb Z-$ modules'?

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#abstract-algebra #modules
2.1k
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On submodules of finitely generated modules over a PID

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#abstract-algebra #modules #principal-ideal-domains

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