Question

Finitely generated free $A$-module is isomorphic to $A^n$

score 1.7k · Answer 1 · 2017-02-01 09:58:15

1.7k

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Finitely generated free $A$-module is isomorphic to $A^n$

Published on 01 Feb 2017 - 9:58

score 668 · Answer 2 · 2017-02-01 15:42:17

668

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Just-infinite quotient in infinite finitely generated group

Published on 01 Feb 2017 - 15:42

score 851 · Answer 3 · 2026-03-26 16:10:17

851

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Let $R$ be an integral domain and $I,J$ be ideals such that $IJ$ is a principal ideal. Then $I$ is finitely generated?

Published on 26 Mar 2026 - 16:10

score 789 · Answer 4 · 2017-02-04 11:09:04

789

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Any module is a union of an increasing chain of finitely generated submodules.

Published on 04 Feb 2017 - 11:09

score 755 · Answer 5 · 2026-03-26 12:53:29

755

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Prove that a free abelian group $A_{n}$ is finitely generated if and only if its rank $n$ is finite

Published on 26 Mar 2026 - 12:53

score 33 · Answer 6 · 2017-02-16 18:25:11

33

Views

Do finitely generated ideals have a "dimension"?

Published on 16 Feb 2017 - 18:25

score 69 · Answer 7 · 2017-03-07 16:32:18

69

Views

Checking whether two elements in $\mathbb{Z}_N \oplus \mathbb{Z}_N$ generate the whole group

Published on 07 Mar 2017 - 16:32

score 40 · Answer 8 · 2017-03-08 17:58:14

40

Views

Let $R$ a ring and $M$ be an $R-$module freely generated by a set $X$, and let $Y$ be a subset of $X$. Show that $Y$ freely generates $RY$

Published on 08 Mar 2017 - 17:58

score 988 · Answer 9 · 2017-03-12 16:18:26

988

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Over a principal ideal domain $R$, a submodule $N$ of a finitely-generated $R-$module M is finitely-generated.

Published on 12 Mar 2017 - 16:18

score 411 · Answer 10 · 2017-03-14 19:39:38

411

Views

For finitely generated abelian groups $A$ and $B$, prove that $A \oplus A \simeq B \oplus B$ implies $A \simeq B$

Published on 14 Mar 2017 - 19:39

score 155 · Answer 11 · 2017-03-16 14:38:36

155

Views

About finite group generated by 2 elements

Published on 16 Mar 2017 - 14:38

score 473 · Answer 12 · 2026-03-27 00:56:02

473

Views

General conditions on generating sets for dihedral groups

Published on 27 Mar 2026 - 0:56

score 132 · Answer 13 · 2017-03-22 07:18:37

132

Views

Show that there is an isomorphism between the 2 modules

Published on 22 Mar 2017 - 7:18

score 1k · Answer 14 · 2017-03-27 17:36:18

1k

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Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$

Published on 27 Mar 2017 - 17:36

score 47 · Answer 15 · 2026-03-26 19:18:51

47

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Quotient of $\langle a,b,c\text{ }|\text{ }a^2bcb^{-1}c^{-1}=1\rangle$ with its commutator

Published on 26 Mar 2026 - 19:18

List Question

Finitely generated free $A$-module is isomorphic to $A^n$

Just-infinite quotient in infinite finitely generated group

Let $R$ be an integral domain and $I,J$ be ideals such that $IJ$ is a principal ideal. Then $I$ is finitely generated?

Any module is a union of an increasing chain of finitely generated submodules.

Prove that a free abelian group $A_{n}$ is finitely generated if and only if its rank $n$ is finite

Do finitely generated ideals have a "dimension"?

Checking whether two elements in $\mathbb{Z}_N \oplus \mathbb{Z}_N$ generate the whole group

Let $R$ a ring and $M$ be an $R-$module freely generated by a set $X$, and let $Y$ be a subset of $X$. Show that $Y$ freely generates $RY$

Over a principal ideal domain $R$, a submodule $N$ of a finitely-generated $R-$module M is finitely-generated.

For finitely generated abelian groups $A$ and $B$, prove that $A \oplus A \simeq B \oplus B$ implies $A \simeq B$

About finite group generated by 2 elements

General conditions on generating sets for dihedral groups

Show that there is an isomorphism between the 2 modules

Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$

Quotient of $\langle a,b,c\text{ }|\text{ }a^2bcb^{-1}c^{-1}=1\rangle$ with its commutator

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