Question

Prove that an abelian group is direct sum of two subgroups.

score 447 · Answer 1 · 2021-01-11 13:11:30

447

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Prove that an abelian group is direct sum of two subgroups.

Published on 11 Jan 2021 - 13:11

score 123 · Answer 2 · 2026-03-28 08:17:16

123

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Extending linear maps on modules.

Published on 28 Mar 2026 - 8:17

score 24 · Answer 3 · 2021-01-12 15:14:44

24

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Specific sum of products from product of sums

Published on 12 Jan 2021 - 15:14

score 110 · Answer 4 · 2026-02-23 05:54:07

110

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If $G=⨝_{i\in I} H_i$ and $K\unlhd G$ is perfect, then $K=⨝_{i\in I}(H_i\cap K)$.

Published on 23 Feb 2026 - 5:54

score 193 · Answer 5 · 2021-01-15 10:28:20

193

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How to calculate this trigonometric sum

Published on 15 Jan 2021 - 10:28

score 54 · Answer 6 · 2021-01-20 00:34:58

54

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How can I direct sum a matrix into the middle of another?

Published on 20 Jan 2021 - 0:34

score 124 · Answer 7 · 2026-03-27 05:41:46

124

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Let $M = K + L$ and let $f: M \to N$ be an epimorphism. Prove that $N = f(K) \oplus f(L)$ if $K \cap L = \operatorname{Ker}f$

Published on 27 Mar 2026 - 5:41

score 89 · Answer 8 · 2021-01-21 02:58:20

89

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Direct sum of two vector spaces

Published on 21 Jan 2021 - 2:58

score 163 · Answer 9 · 2021-01-21 18:29:54

163

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Show that $\mathbb{R}^2$ is a direct sum of subspaces $u,w$

Published on 21 Jan 2021 - 18:29

score 42 · Answer 10 · 2021-01-23 15:53:52

42

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Let $M=K\oplus K'=L\oplus L'$. Prove $K\subset H\leq M$ implies $H=K\oplus (H\cap K')$

Published on 23 Jan 2021 - 15:53

score 33 · Answer 11 · 2021-01-23 20:09:01

33

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$I(\oplus_AM_\alpha)=\oplus_AIM_\alpha$ and $\oplus_AM_\alpha/I(\oplus_AM_\alpha)\cong\oplus_AM_\alpha/IM_\alpha$

Published on 23 Jan 2021 - 20:09

score 36 · Answer 12 · 2021-01-23 21:13:06

36

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Prove that vectorspace is the result of a direct sum

Published on 23 Jan 2021 - 21:13

score 210 · Answer 13 · 2021-01-28 14:19:23

210

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Intuition behind the definition of direct sum of linear subspaces

Published on 28 Jan 2021 - 14:19

score 75 · Answer 14 · 2021-01-28 16:24:17

75

Views

Help with this simple example about projection of linear spaces

Published on 28 Jan 2021 - 16:24

score 121 · Answer 15 · 2021-01-28 18:45:10

121

Views

Help with these statements in Hoffman/Kunze's Linear Algebra book

Published on 28 Jan 2021 - 18:45

List Question

Prove that an abelian group is direct sum of two subgroups.

Extending linear maps on modules.

Specific sum of products from product of sums

If $G=⨝_{i\in I} H_i$ and $K\unlhd G$ is perfect, then $K=⨝_{i\in I}(H_i\cap K)$.

How to calculate this trigonometric sum

How can I direct sum a matrix into the middle of another?

Let $M = K + L$ and let $f: M \to N$ be an epimorphism. Prove that $N = f(K) \oplus f(L)$ if $K \cap L = \operatorname{Ker}f$

Direct sum of two vector spaces

Show that $\mathbb{R}^2$ is a direct sum of subspaces $u,w$

Let $M=K\oplus K'=L\oplus L'$. Prove $K\subset H\leq M$ implies $H=K\oplus (H\cap K')$

$I(\oplus_AM_\alpha)=\oplus_AIM_\alpha$ and $\oplus_AM_\alpha/I(\oplus_AM_\alpha)\cong\oplus_AM_\alpha/IM_\alpha$

Prove that vectorspace is the result of a direct sum

Intuition behind the definition of direct sum of linear subspaces

Help with this simple example about projection of linear spaces

Help with these statements in Hoffman/Kunze's Linear Algebra book

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