Question

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

score 108 · Answer 1 · 2020-07-13 23:29:20

108

Views

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

Published on 13 Jul 2020 - 23:29

score 254 · Answer 2 · 2020-07-23 16:23:44

254

Views

Is every commutative ring isomorphic to a product of directly irreducible rings?

Published on 23 Jul 2020 - 16:23

score 62 · Answer 3 · 2016-08-17 05:50:13

62

Views

A subgroup $A\times B$ of $\mathbb{Z}\times\mathbb{Z}$ with the property that either $A\not <\mathbb{Z}$ or $B\not <\mathbb{Z}$.

Published on 17 Aug 2016 - 5:50

score 846 · Answer 4 · 2026-03-25 22:41:28

846

Views

Why is cohomology the direct product of the $H^n$?

Published on 25 Mar 2026 - 22:41

score 999 · Answer 5 · 2016-08-29 11:02:52

999

Views

$G$ be a group with subgroups $H,K$ such that $G=HK$ , $|H \cap K|=1$ and $H$ is normal in $G$ , then is $K$ also normal in $G$?

Published on 29 Aug 2016 - 11:02

score 175 · Answer 6 · 2016-09-13 18:55:11

175

Views

Why $G=H\times K$ implies $G=H\vee K$?

Published on 13 Sep 2016 - 18:55

score 109 · Answer 7 · 2016-09-17 02:08:53

109

Views

Changing perspective from external to internal direct product...

Published on 17 Sep 2016 - 2:08

score 71 · Answer 8 · 2016-09-23 13:41:47

71

Views

Prove or disprove if $|G|=|K|\neq1$ then the direct product $|G|\times|K|$ will never be a cyclic group

Published on 23 Sep 2016 - 13:41

score 1.9k · Answer 9 · 2016-09-30 14:19:51

1.9k

Views

Generators of a direct product of symmetric groups

Published on 30 Sep 2016 - 14:19

score 629 · Answer 10 · 2016-10-11 09:08:18

629

Views

Some help with this group direct product decomposition

Published on 11 Oct 2016 - 9:08

score 219 · Answer 11 · 2016-10-23 03:19:18

219

Views

Is this a special semidirect product?

Published on 23 Oct 2016 - 3:19

score 71 · Answer 12 · 2026-03-25 13:51:37

71

Views

Prove that $G=\mathbb{Z}_{n_1} \times ... \times \mathbb{Z}_{n_k}$ is cyclic $\iff n_1,...,n_k$ are pairwise coprime

Published on 25 Mar 2026 - 13:51

score 2.2k · Answer 13 · 2016-10-27 23:23:15

2.2k

Views

Order of a direct product of finitely many groups equal to the product of the orders of the groups

Published on 27 Oct 2016 - 23:23

score 143 · Answer 14 · 2016-11-06 18:03:02

143

Views

Prove that it is not necessarily the case that $|Aut(G_{1} \times G_{2})| \leq |Aut(G_{1})|\times |Aut(G_{2})|$

Published on 06 Nov 2016 - 18:03

score 77 · Answer 15 · 2016-11-10 19:41:45

77

Views

Is the direct product of quotient rings left Noetherian?

Published on 10 Nov 2016 - 19:41

List Question

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

Is every commutative ring isomorphic to a product of directly irreducible rings?

A subgroup $A\times B$ of $\mathbb{Z}\times\mathbb{Z}$ with the property that either $A\not <\mathbb{Z}$ or $B\not <\mathbb{Z}$.

Why is cohomology the direct product of the $H^n$?

$G$ be a group with subgroups $H,K$ such that $G=HK$ , $|H \cap K|=1$ and $H$ is normal in $G$ , then is $K$ also normal in $G$?

Why $G=H\times K$ implies $G=H\vee K$?

Changing perspective from external to internal direct product...

Prove or disprove if $|G|=|K|\neq1$ then the direct product $|G|\times|K|$ will never be a cyclic group

Generators of a direct product of symmetric groups

Some help with this group direct product decomposition

Is this a special semidirect product?

Prove that $G=\mathbb{Z}_{n_1} \times ... \times \mathbb{Z}_{n_k}$ is cyclic $\iff n_1,...,n_k$ are pairwise coprime

Order of a direct product of finitely many groups equal to the product of the orders of the groups

Prove that it is not necessarily the case that $|Aut(G_{1} \times G_{2})| \leq |Aut(G_{1})|\times |Aut(G_{2})|$

Is the direct product of quotient rings left Noetherian?

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