List questions from finitely-generated

Published on 25 Mar 2026 - 1:21

71

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

Published on 13 Apr 2026 - 13:47

195

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Categorical Kernel is Module Kernel

Published on 28 Apr 2026 - 18:44

157

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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 05 May 2026 - 3:38

784

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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 13 Apr 2026 - 8:40

1.1k

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

Published on 15 Apr 2026 - 3:04

62

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Characterize Abelian Factor Group to Direct Product

Published on 10 Apr 2026 - 1:07

122

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Isomorphism of finitely generated modules over PIDs

Published on 10 Apr 2026 - 0:40

271

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Show that finitely generated cone in Hilbert space is closed.

Published on 16 Apr 2026 - 1:50

1.1k

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

Published on 25 Mar 2026 - 11:14

106

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

Published on 09 Apr 2026 - 5:52

451

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

Published on 13 Apr 2026 - 23:09

230

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

Published on 14 Apr 2026 - 2:19

588

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

Published on 03 May 2026 - 13:21

45

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

Published on 15 Apr 2026 - 4:38

List Question

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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