Question

Let $p,q$ and $r$ be positive prime numbers. Determine the number of abelian groups of order $p^6q^3r$

score 44 · Answer 1 · 2014-12-09 03:03:38

44

Views

Let $p,q$ and $r$ be positive prime numbers. Determine the number of abelian groups of order $p^6q^3r$

Published on 09 Dec 2014 - 3:03

score 59 · Answer 2 · 2014-12-09 03:52:55

59

Views

Characterize all $\mathbb Z[i]$ modules of order $21$ and $65$

Published on 09 Dec 2014 - 3:52

score 41 · Answer 3 · 2014-12-09 18:16:50

41

Views

Representatives of simple $\mathbb C[\mathbb D_3]$-modules (left modules)

Published on 09 Dec 2014 - 18:16

score 359 · Answer 4 · 2014-12-09 21:20:44

359

Views

Atiyah-MacDonald Ch. 4 exercise 20: what's the module analogue of $\sqrt{\mathfrak{a}+\mathfrak{b}} = \sqrt{\sqrt{\mathfrak{a}}+\sqrt{\mathfrak{b}}}$?

Published on 09 Dec 2014 - 21:20

score 444 · Answer 5 · 2014-12-10 03:55:44

444

Views

Group presentation and Smith normal form

Published on 10 Dec 2014 - 3:55

score 288 · Answer 6 · 2014-12-10 05:54:46

288

Views

Finitely generated modules over a PIR (structure theorem application)

Published on 10 Dec 2014 - 5:54

score 493 · Answer 7 · 2014-12-10 14:00:25

493

Views

If $M/N$ is isomorphic to $M/N'$, can we conclude that $N$ is isomorphic to $N'$?

Published on 10 Dec 2014 - 14:00

score 899 · Answer 8 · 2014-12-10 14:33:47

899

Views

Let $R=M_n(D)$, $D$ is a division ring. Prove that every $R-$simple module is isomorphic to each other.

Published on 10 Dec 2014 - 14:33

score 1.2k · Answer 9 · 2026-03-26 02:52:35

1.2k

Views

Exact sequence and Noetherian modules

Published on 26 Mar 2026 - 2:52

score 316 · Answer 10 · 2014-12-11 00:03:14

316

Views

Constructing pullback and pushout problem

Published on 11 Dec 2014 - 0:03

score 437 · Answer 11 · 2014-12-10 23:40:40

437

Views

Are two bimodules isomomorphic as left and right modules also isomorphic as bimodules?

Published on 10 Dec 2014 - 23:40

score 701 · Answer 12 · 2014-12-11 07:08:27

701

Views

Finite abelian groups (application of structure theorem)

Published on 11 Dec 2014 - 7:08

score 831 · Answer 13 · 2026-03-26 17:33:31

831

Views

Showing that $0 \to \mathrm{Hom}(M, M_1) \to \mathrm{Hom}_R(M, M_2) \to \mathrm{Hom}(M, M_3)$ is exact

Published on 26 Mar 2026 - 17:33

score 57 · Answer 14 · 2014-12-12 01:52:36

57

Views

Simple problem about morphism in abelian categories

Published on 12 Dec 2014 - 1:52

score 479 · Answer 15 · 2014-12-12 01:53:21

479

Views

Semisimplicity of the ring $\mathbb Z_n$

Published on 12 Dec 2014 - 1:53

List Question

Let $p,q$ and $r$ be positive prime numbers. Determine the number of abelian groups of order $p^6q^3r$

Characterize all $\mathbb Z[i]$ modules of order $21$ and $65$

Representatives of simple $\mathbb C[\mathbb D_3]$-modules (left modules)

Atiyah-MacDonald Ch. 4 exercise 20: what's the module analogue of $\sqrt{\mathfrak{a}+\mathfrak{b}} = \sqrt{\sqrt{\mathfrak{a}}+\sqrt{\mathfrak{b}}}$?

Group presentation and Smith normal form

Finitely generated modules over a PIR (structure theorem application)

If $M/N$ is isomorphic to $M/N'$, can we conclude that $N$ is isomorphic to $N'$?

Let $R=M_n(D)$, $D$ is a division ring. Prove that every $R-$simple module is isomorphic to each other.

Exact sequence and Noetherian modules

Constructing pullback and pushout problem

Are two bimodules isomomorphic as left and right modules also isomorphic as bimodules?

Finite abelian groups (application of structure theorem)

Showing that $0 \to \mathrm{Hom}(M, M_1) \to \mathrm{Hom}_R(M, M_2) \to \mathrm{Hom}(M, M_3)$ is exact

Simple problem about morphism in abelian categories

Semisimplicity of the ring $\mathbb Z_n$

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