Question

Prove that if the induced homomorphism $M/\mathfrak aM \to N/\mathfrak aN$ is surjective, then $f$ it's surjective.

score 1.1k · Answer 1 · 2014-07-03 10:41:38

1.1k

Views

Prove that if the induced homomorphism $M/\mathfrak aM \to N/\mathfrak aN$ is surjective, then $f$ it's surjective.

Published on 03 Jul 2014 - 10:41

score 589 · Answer 2 · 2014-07-06 08:36:52

589

Views

What are all the automorphisms of a group of order $9$ generated by two elements?

Published on 06 Jul 2014 - 8:36

score 1.1k · Answer 3 · 2014-07-07 12:10:10

1.1k

Views

Subgroups of $\mathrm{GL}(n,\mathbb{Z})$ which are not finitely generated

Published on 07 Jul 2014 - 12:10

score 4.2k · Answer 4 · 2014-07-17 14:36:27

4.2k

Views

Finitely generated ring.

Published on 17 Jul 2014 - 14:36

score 1.2k · Answer 5 · 2014-07-19 07:56:41

1.2k

Views

Finitely-generated group such that all (non-trivial) normal subgroups have finite index implies all (non-trivial) subgroups have finite index?

Published on 19 Jul 2014 - 7:56

score 210 · Answer 6 · 2014-07-21 09:13:02

210

Views

Finitely generated, periodic group such that each conjugacy class is finite must be finite?

Published on 21 Jul 2014 - 9:13

score 1.5k · Answer 7 · 2014-07-22 13:54:37

1.5k

Views

Surjectivity implies injectivity of finitely generated modules, localization?

Published on 22 Jul 2014 - 13:54

score 952 · Answer 8 · 2014-07-27 16:41:13

952

Views

The ring $R$ is a field iff $R$ has a finitely generated divisible module

Published on 27 Jul 2014 - 16:41

score 120 · Answer 9 · 2014-09-01 05:21:09

120

Views

Are there any commutative rings in which no nonzero prime ideal is finitely generated?

Published on 01 Sep 2014 - 5:21

score 105 · Answer 10 · 2026-03-25 22:11:19

105

Views

Finitely generated group $G$ such that $G\cong G*G$ must be trivial

Published on 25 Mar 2026 - 22:11

score 210 · Answer 11 · 2014-09-15 13:56:54

210

Views

If the factor of a finitely generated module is free then submodule is also finitely generated

Published on 15 Sep 2014 - 13:56

score 555 · Answer 12 · 2026-03-25 17:32:10

555

Views

Conditions for a finitely generated group with finite ordered generators

Published on 25 Mar 2026 - 17:32

score 158 · Answer 13 · 2014-09-19 10:27:53

158

Views

Generator of a subalgebra over a ring

Published on 19 Sep 2014 - 10:27

score 195 · Answer 14 · 2026-03-25 19:05:30

195

Views

Showing the full transformation semigroup $\mathscr{T}_n=\langle\zeta, \tau, \pi\rangle$.

Published on 25 Mar 2026 - 19:05

score 226 · Answer 15 · 2014-09-30 18:06:14

226

Views

A relation involving an endomorphism of a finitely generated module

Published on 30 Sep 2014 - 18:06

List Question

Prove that if the induced homomorphism $M/\mathfrak aM \to N/\mathfrak aN$ is surjective, then $f$ it's surjective.

What are all the automorphisms of a group of order $9$ generated by two elements?

Subgroups of $\mathrm{GL}(n,\mathbb{Z})$ which are not finitely generated

Finitely generated ring.

Finitely-generated group such that all (non-trivial) normal subgroups have finite index implies all (non-trivial) subgroups have finite index?

Finitely generated, periodic group such that each conjugacy class is finite must be finite?

Surjectivity implies injectivity of finitely generated modules, localization?

The ring $R$ is a field iff $R$ has a finitely generated divisible module

Are there any commutative rings in which no nonzero prime ideal is finitely generated?

Finitely generated group $G$ such that $G\cong G*G$ must be trivial

If the factor of a finitely generated module is free then submodule is also finitely generated

Conditions for a finitely generated group with finite ordered generators

Generator of a subalgebra over a ring

Showing the full transformation semigroup $\mathscr{T}_n=\langle\zeta, \tau, \pi\rangle$.

A relation involving an endomorphism of a finitely generated module

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