Question

How can I prove that $2\mathbb{Z}$ is NOT a direct summand of $\mathbb{Z}$, as $\mathbb{Z}$-modules?

score 273 · Answer 1 · 2016-05-02 13:01:04

273

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How can I prove that $2\mathbb{Z}$ is NOT a direct summand of $\mathbb{Z}$, as $\mathbb{Z}$-modules?

Published on 02 May 2016 - 13:01

score 718 · Answer 2 · 2016-05-03 11:59:25

718

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V as a direct sum of T-Invariant subspaces

Published on 03 May 2016 - 11:59

score 1.9k · Answer 3 · 2026-03-28 05:28:58

1.9k

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direct sum of noetherian modules is noetherian

Published on 28 Mar 2026 - 5:28

score 339 · Answer 4 · 2016-06-12 05:28:41

339

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Expressing an $R$-module as a direct sum

Published on 12 Jun 2016 - 5:28

score 4.1k · Answer 5 · 2016-06-15 13:57:00

4.1k

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Direct sum of vector subspaces equals $\mathbb R^3$

Published on 15 Jun 2016 - 13:57

score 413 · Answer 6 · 2016-06-16 17:19:35

413

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Radical of a direct sum of Lie algebra

Published on 16 Jun 2016 - 17:19

score 2.5k · Answer 7 · 2026-03-28 01:24:05

2.5k

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Meaning of $Z\oplus Z$

Published on 28 Mar 2026 - 1:24

score 61 · Answer 8 · 2016-06-17 22:08:43

61

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Example of an abelian group $G$ with $A \le G$ but no $B \le G$ with $G = A \oplus B$.

Published on 17 Jun 2016 - 22:08

score 46 · Answer 9 · 2016-06-18 07:00:42

46

Views

Expressing $\mathbb{C}^3$ as a direct sum

Published on 18 Jun 2016 - 7:00

score 496 · Answer 10 · 2016-06-22 00:25:46

496

Views

Real Analysis, Folland Proposition 2.13 Integration of Nonnegative Functions

Published on 22 Jun 2016 - 0:25

score 1.2k · Answer 11 · 2016-06-26 18:33:26

1.2k

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How to find a subgroup of the external direct product $\Bbb{Z}/4\Bbb{Z}\oplus\Bbb{Z}/2\Bbb{Z}$ not of the form $H\oplus K$?

Published on 26 Jun 2016 - 18:33

score 270 · Answer 12 · 2016-07-04 23:50:54

270

Views

Invariant subspaces under T and polynomials

Published on 04 Jul 2016 - 23:50

score 1k · Answer 13 · 2013-05-14 18:31:07

1k

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Abelian categories with direct sums

Published on 14 May 2013 - 18:31

score 1.6k · Answer 14 · 2013-05-29 00:27:25

1.6k

Views

A complex lie algebra is the direct sum of simple ideals iff it is semisimple

Published on 29 May 2013 - 0:27

score 2.5k · Answer 15 · 2013-09-28 23:57:00

2.5k

Views

When do you use the internal vs. external direct sum of groups?

Published on 28 Sep 2013 - 23:57

List Question

How can I prove that $2\mathbb{Z}$ is NOT a direct summand of $\mathbb{Z}$, as $\mathbb{Z}$-modules?

V as a direct sum of T-Invariant subspaces

direct sum of noetherian modules is noetherian

Expressing an $R$-module as a direct sum

Direct sum of vector subspaces equals $\mathbb R^3$

Radical of a direct sum of Lie algebra

Meaning of $Z\oplus Z$

Example of an abelian group $G$ with $A \le G$ but no $B \le G$ with $G = A \oplus B$.

Expressing $\mathbb{C}^3$ as a direct sum

Real Analysis, Folland Proposition 2.13 Integration of Nonnegative Functions

How to find a subgroup of the external direct product $\Bbb{Z}/4\Bbb{Z}\oplus\Bbb{Z}/2\Bbb{Z}$ not of the form $H\oplus K$?

Invariant subspaces under T and polynomials

Abelian categories with direct sums

A complex lie algebra is the direct sum of simple ideals iff it is semisimple

When do you use the internal vs. external direct sum of groups?

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