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Finitely generated k-algebra is Noetherian

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#algebraic-geometry #noetherian #finitely-generated
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Product of commutators in a group with abelian commutator subgroup

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#group-theory #finitely-generated
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If the tensor product of two modules is free of finite rank, then the modules are finitely generated and projective

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#abstract-algebra #commutative-algebra #modules #projective-module #finitely-generated
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Free $A$-module isomorphic to a direct sum of copies of $A$?

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#abstract-algebra #modules #self-learning #finitely-generated
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Finitely generated graded modules over $K[x]$

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#abstract-algebra #principal-ideal-domains #finitely-generated #graded-modules
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Finitely generated group that doesn't satisfy ACC condition.

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#abstract-algebra #group-theory #finitely-generated
214
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Rank of finitely generated abelian groups

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#abstract-algebra #group-theory #finitely-generated
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Any non-trivial finitely-generated group admits maximal subgroups

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#abstract-algebra #group-theory #solution-verification #finitely-generated #maximal-subgroup
192
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Choice of ideal so that localisation of a module must be free?

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#commutative-algebra #modules #noetherian #finitely-generated
46
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Is the image of Spec$k$ closed under these conditions?

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#schemes #finitely-generated
118
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Algebra extension of modules question

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#abstract-algebra #modules #finitely-generated
320
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How to construct a nonzero homomorphism from a module to a proper submodule?

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#commutative-algebra #modules #abstract-algebra #finitely-generated
48
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Example of non finitely-generated $R$-Module $K$ so that $K/PK$ is finitely generated

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#commutative-algebra #finitely-generated
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the automorphism group of a finitely generated group

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#abstract-algebra #group-theory #finitely-generated
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A field is finite if and only if its multiplicative group is finitely generated.

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#abstract-algebra #field-theory #finite-fields #finitely-generated

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