List questions from finitely-generated

Published on 25 Mar 2026 - 1:21

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maximal $R$-linearly independent subset of a finitely generated module

Published on 12 Aug 2018 - 21:52

189

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Categorical Kernel is Module Kernel

Published on 19 Aug 2018 - 6:30

153

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If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

Published on 20 Aug 2018 - 0:35

782

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Show that the ring of polynomials with coefficients in a field, and in infinitely many variables, is not Noetherian

Published on 25 Mar 2026 - 6:06

1.1k

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A group with finitely generated normal subgroup and finitely generated quotient is finitely generated itself

Published on 25 Aug 2018 - 11:57

59

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Characterize Abelian Factor Group to Direct Product

Published on 26 Aug 2018 - 7:58

119

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Isomorphism of finitely generated modules over PIDs

Published on 13 Sep 2018 - 17:38

269

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Show that finitely generated cone in Hilbert space is closed.

Published on 25 Mar 2026 - 1:41

1.1k

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Torsion subgroup of a finitely-generated abelian group is finite?

Published on 03 Oct 2018 - 8:06

103

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How many elements generate the cyclic group $\mathbb{Z}/p^r\mathbb{Z}$?

Published on 04 Oct 2018 - 14:28

449

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Exists a discrete isometry group that's not finitely generated?

Published on 25 Mar 2026 - 7:42

227

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Exists a discrete Euclidean isometry group that's not finitely generated?

Published on 24 Oct 2018 - 16:29

585

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The kernel of a surjective homomorphism $G\rightarrow\mathbb{Z}$ is finitely generated

Published on 22 Mar 2026 - 11:49

42

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Prove that every finitely generated subgroup of a totally ordered group can be totally ordered.

Published on 04 Nov 2018 - 21:11

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What interesting properties does $A^3$ have?

maximal $R$-linearly independent subset of a finitely generated module

Categorical Kernel is Module Kernel

If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

Show that the ring of polynomials with coefficients in a field, and in infinitely many variables, is not Noetherian

A group with finitely generated normal subgroup and finitely generated quotient is finitely generated itself

Characterize Abelian Factor Group to Direct Product

Isomorphism of finitely generated modules over PIDs

Show that finitely generated cone in Hilbert space is closed.

Torsion subgroup of a finitely-generated abelian group is finite?

How many elements generate the cyclic group $\mathbb{Z}/p^r\mathbb{Z}$?

Exists a discrete isometry group that's not finitely generated?

Exists a discrete Euclidean isometry group that's not finitely generated?

The kernel of a surjective homomorphism $G\rightarrow\mathbb{Z}$ is finitely generated

Prove that every finitely generated subgroup of a totally ordered group can be totally ordered.

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