Question

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

score 251 · Answer 1 · 2026-03-25 16:08:37

251

Views

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

Published on 25 Mar 2026 - 16:08

score 67 · Answer 2 · 2026-03-23 00:55:38

67

Views

Find inner product that meets primary decomposition criterias

Published on 23 Mar 2026 - 0:55

score 31 · Answer 3 · 2026-03-25 16:07:02

31

Views

Dual terminology to "component function"?

Published on 25 Mar 2026 - 16:07

score 126 · Answer 4 · 2018-07-01 03:07:11

126

Views

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

Published on 01 Jul 2018 - 3:07

score 167 · Answer 5 · 2018-08-03 22:34:48

167

Views

Representation of elements of direct sum of groups

Published on 03 Aug 2018 - 22:34

score 74 · Answer 6 · 2018-08-15 01:29:26

74

Views

Naturality of torsion distributing over direct sum

Published on 15 Aug 2018 - 1:29

score 154 · Answer 7 · 2026-03-25 11:16:38

154

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 25 Mar 2026 - 11:16

score 170 · Answer 8 · 2026-03-26 07:35:24

170

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 26 Mar 2026 - 7:35

score 3.3k · Answer 9 · 2018-08-24 13:57:12

3.3k

Views

Summation with multiple variables seprated by comma.

Published on 24 Aug 2018 - 13:57

score 56 · Answer 10 · 2018-08-31 10:52:46

56

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 31 Aug 2018 - 10:52

score 295 · Answer 11 · 2026-03-25 17:45:12

295

Views

Why is a direct summand of a compact object compact?

Published on 25 Mar 2026 - 17:45

score 89 · Answer 12 · 2018-09-15 13:13:27

89

Views

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

Published on 15 Sep 2018 - 13:13

score 642 · Answer 13 · 2026-03-25 08:09:20

642

Views

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

Published on 25 Mar 2026 - 8:09

score 88 · Answer 14 · 2026-03-24 20:38:03

88

Views

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

Published on 24 Mar 2026 - 20:38

score 105 · Answer 15 · 2018-09-30 17:13:02

105

Views

Direct sum of groups categorically

Published on 30 Sep 2018 - 17:13

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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