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Group direct sum construction. Problem from Undergraduate Algebra by Serge Lang.

score 116 · Answer 1 · 2026-03-27 23:39:46

116

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Group direct sum construction. Problem from Undergraduate Algebra by Serge Lang.

Published on 27 Mar 2026 - 23:39

score 2.4k · Answer 2 · 2015-11-01 00:11:21

2.4k

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For a direct sum of modules, can the two modules be the same?

Published on 01 Nov 2015 - 0:11

score 72 · Answer 3 · 2015-11-01 14:37:23

72

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Two quotients of projective modules are equal, prove the crossed direct sums of the projective modules and kernels are isomorphic. (Schanuel's Lemma)

Published on 01 Nov 2015 - 14:37

score 207 · Answer 4 · 2015-11-02 21:44:48

207

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Properties of a module that is an internal direct sum

Published on 02 Nov 2015 - 21:44

score 63 · Answer 5 · 2015-11-04 23:28:21

63

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The sum of integer parts of $2k/n$ over $k=1,\dots,n-1$

Published on 04 Nov 2015 - 23:28

score 59 · Answer 6 · 2015-11-09 07:49:05

59

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Direct Sum Computation

Published on 09 Nov 2015 - 7:49

score 43 · Answer 7 · 2015-11-10 10:09:54

43

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Problem with direct sums

Published on 10 Nov 2015 - 10:09

score 3.2k · Answer 8 · 2015-11-19 04:39:50

3.2k

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Dual space of arbitrary direct sum is the direct sum of dual spaces

Published on 19 Nov 2015 - 4:39

score 685 · Answer 9 · 2015-12-03 21:38:30

685

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Definition of direct sum

Published on 03 Dec 2015 - 21:38

score 147 · Answer 10 · 2015-12-13 00:39:05

147

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Doubts regarding the sum of vector subspaces

Published on 13 Dec 2015 - 0:39

score 1.3k · Answer 11 · 2015-12-14 19:16:19

1.3k

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Module which is not direct sum of indecomposable submodules

Published on 14 Dec 2015 - 19:16

score 333 · Answer 12 · 2015-12-15 09:18:53

333

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Finding the kernel of a linear operator involving direct sum

Published on 15 Dec 2015 - 9:18

score 33 · Answer 13 · 2026-03-27 07:50:27

33

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Relation between direct product and direct sum of $S_{N_1} \wr D_{m_1}, \ldots, S_{N_t} \wr D_{m_t}$

Published on 27 Mar 2026 - 7:50

score 229 · Answer 14 · 2026-03-23 01:33:40

229

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Exponent of the direct sum of finite groups, specifically, $\sum^t_i S_{N_i} \wr D_{m_i}$

Published on 23 Mar 2026 - 1:33

score 1k · Answer 15 · 2015-12-20 17:44:36

1k

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Direct sum proof: If the union of the basis of $W_1,W_2,...,W_k$ is a basis of $V$ than $W_1 \oplus W_2 \oplus ... \oplus W_k= V$

Published on 20 Dec 2015 - 17:44

List Question

Group direct sum construction. Problem from Undergraduate Algebra by Serge Lang.

For a direct sum of modules, can the two modules be the same?

Two quotients of projective modules are equal, prove the crossed direct sums of the projective modules and kernels are isomorphic. (Schanuel's Lemma)

Properties of a module that is an internal direct sum

The sum of integer parts of $2k/n$ over $k=1,\dots,n-1$

Direct Sum Computation

Problem with direct sums

Dual space of arbitrary direct sum is the direct sum of dual spaces

Definition of direct sum

Doubts regarding the sum of vector subspaces

Module which is not direct sum of indecomposable submodules

Finding the kernel of a linear operator involving direct sum

Relation between direct product and direct sum of $S_{N_1} \wr D_{m_1}, \ldots, S_{N_t} \wr D_{m_t}$

Exponent of the direct sum of finite groups, specifically, $\sum^t_i S_{N_i} \wr D_{m_i}$

Direct sum proof: If the union of the basis of $W_1,W_2,...,W_k$ is a basis of $V$ than $W_1 \oplus W_2 \oplus ... \oplus W_k= V$

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