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This defines an equivalence of categories between the category of algebraic sets and the opposite category of the finitely generated reduced "k" -algebras.
en.wikipedia.org These groups are finitely generated, but not finitely presented.
en.wikipedia.org This follows from the classification of finitely generated abelian groups.
en.wikipedia.org His most famous result is that the ring of invariants of binary forms of fixed degree is finitely generated.
en.wikipedia.org Another important idea in geometric group theory is to consider finitely generated groups themselves as geometric objects.
en.wikipedia.org