Question

Module is semisimple if and only if M is the sum of simple submodules.

score 407 · Answer 1 · 2026-04-09 08:07:57

407

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Module is semisimple if and only if M is the sum of simple submodules.

Published on 09 Apr 2026 - 8:07

score 213 · Answer 2 · 2026-04-12 04:32:12

213

Views

Projection of Submodules

Published on 12 Apr 2026 - 4:32

score 449 · Answer 3 · 2026-04-09 18:10:24

449

Views

Closure of direct sum and direct sum of the closure

Published on 09 Apr 2026 - 18:10

score 844 · Answer 4 · 2026-05-10 20:08:26

844

Views

Is an abelian group the sum of a torsion group with a free group?

Published on 10 May 2026 - 20:08

score 51 · Answer 5 · 2026-04-12 19:42:50

51

Views

Restriction of linear operator and nonsingularity

Published on 12 Apr 2026 - 19:42

score 103 · Answer 6 · 2026-04-14 03:56:20

103

Views

Is $\Lambda(T^{}E)=\bigoplus_{k=0}^n\Lambda^k(T^{}E)$ a complex line bundle over $T^{*}E$?

Published on 14 Apr 2026 - 3:56

score 2.7k · Answer 7 · 2026-04-17 03:45:40

2.7k

Views

Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$

Published on 17 Apr 2026 - 3:45

score 1.2k · Answer 8 · 2026-04-14 11:42:18

1.2k

Views

Does exact sequence of abelian groups split when middle group has a subgroup direct sum of other groups?

Published on 14 Apr 2026 - 11:42

score 125 · Answer 9 · 2026-04-11 14:59:43

125

Views

Generating an algebra

Published on 11 Apr 2026 - 14:59

score 129 · Answer 10 · 2026-04-15 09:20:44

129

Views

Proof that Vector Space in Domain of Linear Map is a Direct Sum

Published on 15 Apr 2026 - 9:20

score 740 · Answer 11 · 2026-04-14 11:47:41

740

Views

Sum and difference of projections

Published on 14 Apr 2026 - 11:47

score 495 · Answer 12 · 2026-04-13 23:58:38

495

Views

Does the tensor product distribute over internal direct sums as well?

Published on 13 Apr 2026 - 23:58

score 2.3k · Answer 13 · 2026-04-17 11:53:53

2.3k

Views

Direct-sum decomposition of dual space

Published on 17 Apr 2026 - 11:53

score 629 · Answer 14 · 2026-04-13 16:15:48

629

Views

Given two linear transformations, prove that V is equal to the direct sum of the kernels.

Published on 13 Apr 2026 - 16:15

score 2.6k · Answer 15 · 2026-04-10 00:04:18

2.6k

Views

distributivity of tensor product and direct sum for Hilbert spaces

Published on 10 Apr 2026 - 0:04

List Question

Module is semisimple if and only if M is the sum of simple submodules.

Projection of Submodules

Closure of direct sum and direct sum of the closure

Is an abelian group the sum of a torsion group with a free group?

Restriction of linear operator and nonsingularity

Is $\Lambda(T^{}E)=\bigoplus_{k=0}^n\Lambda^k(T^{}E)$ a complex line bundle over $T^{*}E$?

Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$

Does exact sequence of abelian groups split when middle group has a subgroup direct sum of other groups?

Generating an algebra

Proof that Vector Space in Domain of Linear Map is a Direct Sum

Sum and difference of projections

Does the tensor product distribute over internal direct sums as well?

Direct-sum decomposition of dual space

Given two linear transformations, prove that V is equal to the direct sum of the kernels.

distributivity of tensor product and direct sum for Hilbert spaces

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