Question

Why does the direct sum of infinitely many groups require only finitely many are nonzero?

score 255 · Answer 1 · 2026-05-10 14:56:20

255

Views

Why does the direct sum of infinitely many groups require only finitely many are nonzero?

Published on 10 May 2026 - 14:56

score 76 · Answer 2 · 2026-05-05 14:04:01

76

Views

Find inner product that meets primary decomposition criterias

Published on 05 May 2026 - 14:04

score 35 · Answer 3 · 2026-05-10 14:47:35

35

Views

Dual terminology to "component function"?

Published on 10 May 2026 - 14:47

score 130 · Answer 4 · 2026-05-05 04:28:18

130

Views

$\mathbb R^{+}$ is isomorphic to $2^{\aleph}$ copies of $\mathbb Q$

Published on 05 May 2026 - 4:28

score 171 · Answer 5 · 2026-05-06 14:38:23

171

Views

Representation of elements of direct sum of groups

Published on 06 May 2026 - 14:38

score 80 · Answer 6 · 2026-05-07 14:25:56

80

Views

Naturality of torsion distributing over direct sum

Published on 07 May 2026 - 14:25

score 158 · Answer 7 · 2026-05-10 15:30:17

158

Views

If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

Published on 10 May 2026 - 15:30

score 172 · Answer 8 · 2026-04-15 21:15:42

172

Views

Check My Proof - $V = \sum_{i = 1}^{n} U_i \implies V = \bigoplus_{i = 1}^{n} U_i$ if $U_i \bot U_j \ \forall i,j \in \{1, \ldots, n\}$

Published on 15 Apr 2026 - 21:15

score 3.3k · Answer 9 · 2026-05-05 15:46:02

3.3k

Views

Summation with multiple variables seprated by comma.

Published on 05 May 2026 - 15:46

score 60 · Answer 10 · 2026-05-05 12:24:44

60

Views

Injectivity and surjectivity of $\prod_{i=1}^m W_i \to \sum_{i=1}^m W_i$ given by $(w_i)_i \mapsto \sum_i w_i$

Published on 05 May 2026 - 12:24

score 301 · Answer 11 · 2026-05-10 13:49:04

301

Views

Why is a direct summand of a compact object compact?

Published on 10 May 2026 - 13:49

score 92 · Answer 12 · 2026-04-15 04:12:43

92

Views

Ideals of $R = R_1 \oplus R_2 \oplus \dots \oplus R_n$

Published on 15 Apr 2026 - 4:12

score 645 · Answer 13 · 2026-05-05 10:16:20

645

Views

Finding the projections associated to the direct sum decomposition of a vector space

Published on 05 May 2026 - 10:16

score 92 · Answer 14 · 2026-05-10 12:53:36

92

Views

Explaining the $K$ functor isomorphism $K(X) \cong \tilde{K}(X) \oplus \Bbb Z$

Published on 10 May 2026 - 12:53

score 109 · Answer 15 · 2026-05-06 14:20:33

109

Views

Direct sum of groups categorically

Published on 06 May 2026 - 14:20

List Question

Why does the direct sum of infinitely many groups require only finitely many are nonzero?

Find inner product that meets primary decomposition criterias

Dual terminology to "component function"?

$\mathbb R^{+}$ is isomorphic to $2^{\aleph}$ copies of $\mathbb Q$

Representation of elements of direct sum of groups

Naturality of torsion distributing over direct sum

If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

Check My Proof - $V = \sum_{i = 1}^{n} U_i \implies V = \bigoplus_{i = 1}^{n} U_i$ if $U_i \bot U_j \ \forall i,j \in \{1, \ldots, n\}$

Summation with multiple variables seprated by comma.

Injectivity and surjectivity of $\prod_{i=1}^m W_i \to \sum_{i=1}^m W_i$ given by $(w_i)_i \mapsto \sum_i w_i$

Why is a direct summand of a compact object compact?

Ideals of $R = R_1 \oplus R_2 \oplus \dots \oplus R_n$

Finding the projections associated to the direct sum decomposition of a vector space

Explaining the $K$ functor isomorphism $K(X) \cong \tilde{K}(X) \oplus \Bbb Z$

Direct sum of groups categorically

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