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Does there exist such a subspace?

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#linear-algebra #vector-spaces #complex-numbers #vectors #direct-sum
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An example of direct sum

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#linear-algebra #direct-sum
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The existence of the direct sum

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#linear-algebra #vector-spaces #direct-sum
168
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Show $\phi(B)/\phi(A)\cong B/A\oplus(B\cap\ker\phi)$

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#proof-verification #modules #direct-sum #module-isomorphism
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Cancellation law for direct sums

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#linear-algebra #direct-sum
200
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Relation between invariant subspaces and direct sums

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#linear-algebra #direct-sum #invariant-subspace
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Group of units of direct sum of rings is isomorphic to direct sum of the groups of units

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#abstract-algebra #ring-theory #group-isomorphism #direct-sum
1.6k
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Modules, Direct Sums, Confusion

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#modules #direct-sum
283
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Direct sum of isomorphic modules

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#modules #direct-sum
54
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How to compute the $\frac{x}{x_1} \cdot x_2 + \frac{y}{y_1} \cdot y_2$

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#algebra-precalculus #direct-sum
335
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Statement on an abelian group being isomorphic to a direct sum of cyclic groups

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#abelian-groups #cyclic-groups #direct-sum #direct-product
45
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Decomposition of $\mathbb{M}^2(\mathbb{R})$

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#linear-algebra #matrices #vector-spaces #direct-sum
39
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Difficulty with characterization of semisimplicity in terms of complements

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#abstract-algebra #modules #abelian-categories #direct-sum #direct-product
212
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The functor $\mathrm{Hom}(A,-)$ cannot commute with arbitrary direct sums for infinitely generated projective module $A$

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#abstract-algebra #modules #direct-sum #projective-module
49
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What are $e_1, e_2, h_1$ and $h_2 \ ?$

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#vector-spaces #direct-sum

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