Question

Why $M/\mathfrak{a}M \oplus M/\mathfrak{b}M \simeq M/(\mathfrak{a \cap b})M$?

score 117 · Answer 1 · 2026-03-25 14:22:07

117

Views

Why $M/\mathfrak{a}M \oplus M/\mathfrak{b}M \simeq M/(\mathfrak{a \cap b})M$?

Published on 25 Mar 2026 - 14:22

score 43 · Answer 2 · 2020-06-27 23:28:39

43

Views

Understanding the direct sum of two subspaces

Published on 27 Jun 2020 - 23:28

score 763 · Answer 3 · 2020-06-28 06:44:43

763

Views

Prove the direct sum of the sets of odd and even functions is $\mathbb{R^{R}}$

Published on 28 Jun 2020 - 6:44

score 36 · Answer 4 · 2026-03-26 18:04:43

36

Views

One of a math problems

Published on 26 Mar 2026 - 18:04

score 174 · Answer 5 · 2026-03-25 22:38:40

174

Views

Let $R$ be a ring of $2\times2$ upper triangular matrices over $\Bbb Z2$. I need to list all direct summands of left $R$-module $R$.

Published on 25 Mar 2026 - 22:38

score 24 · Answer 6 · 2020-07-01 18:14:36

24

Views

number of submodules of direct sum of simple modules

Published on 01 Jul 2020 - 18:14

score 107 · Answer 7 · 2020-07-10 17:21:03

107

Views

A question in a theorem of section 6.6 of Hoffman Kunze

Published on 10 Jul 2020 - 17:21

score 193 · Answer 8 · 2020-07-13 14:58:53

193

Views

Strengthened Cauchy-Schwarz and direct sum

Published on 13 Jul 2020 - 14:58

score 109 · Answer 9 · 2026-03-26 17:37:16

109

Views

Modifying $\frac{\prod_\alpha A_\alpha}{\prod_\alpha B_\alpha}\simeq \prod_\alpha\frac{A_\alpha}{B_\alpha}$ for direct sums

Published on 26 Mar 2026 - 17:37

score 323 · Answer 10 · 2020-07-15 13:14:57

323

Views

Does $\ker T\cap {\rm Im}\,T=\{0\}$ imply $V=\ker T\oplus{\rm Im}\,T$?

Published on 15 Jul 2020 - 13:14

score 5.8k · Answer 11 · 2016-07-16 20:53:03

5.8k

Views

Is it true that if $T$ is a linear operator on a finite-dimensional vector space $V$ then $V=\ker T\oplus \operatorname{im}T$?

Published on 16 Jul 2016 - 20:53

score 963 · Answer 12 · 2026-03-26 05:54:39

963

Views

Minimal ideal in a ring which is generated by an idempotent element.

Published on 26 Mar 2026 - 5:54

score 3.6k · Answer 13 · 2016-07-27 23:10:55

3.6k

Views

Multiplication in Direct Sum of Algebras

Published on 27 Jul 2016 - 23:10

score 6.6k · Answer 14 · 2016-07-28 01:35:44

6.6k

Views

If $T$ and $T^2$ have equal rank then $V=\ker T\oplus {\rm im}\, T$ for $V$ finite dimensional.

Published on 28 Jul 2016 - 1:35

score 160 · Answer 15 · 2016-08-02 20:16:05

160

Views

Is it possible to have $G\oplus H \simeq G$ for abelian groups $G$ and $H$.

Published on 02 Aug 2016 - 20:16

List Question

Why $M/\mathfrak{a}M \oplus M/\mathfrak{b}M \simeq M/(\mathfrak{a \cap b})M$?

Understanding the direct sum of two subspaces

Prove the direct sum of the sets of odd and even functions is $\mathbb{R^{R}}$

One of a math problems

Let $R$ be a ring of $2\times2$ upper triangular matrices over $\Bbb Z2$. I need to list all direct summands of left $R$-module $R$.

number of submodules of direct sum of simple modules

A question in a theorem of section 6.6 of Hoffman Kunze

Strengthened Cauchy-Schwarz and direct sum

Modifying $\frac{\prod_\alpha A_\alpha}{\prod_\alpha B_\alpha}\simeq \prod_\alpha\frac{A_\alpha}{B_\alpha}$ for direct sums

Does $\ker T\cap {\rm Im}\,T=\{0\}$ imply $V=\ker T\oplus{\rm Im}\,T$?

Is it true that if $T$ is a linear operator on a finite-dimensional vector space $V$ then $V=\ker T\oplus \operatorname{im}T$?

Minimal ideal in a ring which is generated by an idempotent element.

Multiplication in Direct Sum of Algebras

If $T$ and $T^2$ have equal rank then $V=\ker T\oplus {\rm im}\, T$ for $V$ finite dimensional.

Is it possible to have $G\oplus H \simeq G$ for abelian groups $G$ and $H$.

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