The space of finitely generated rings

Details The space of finitely generated rings The space of finitely generated rings

2009-04-27

arxiv.org/abs/0904.4216v1

Internat. J. Algebra Comput. 19(3) (2009) 373-382

Mathematics

Commutative Algebra

10 pages, no figure. To appear in Internat. J. Algebra Comput

Scientific paper

10.1142/S0218196709005068

The space of marked commutative rings on n given generators is a compact metrizable space. We compute the Cantor-Bendixson rank of any member of this space. For instance, the Cantor-Bendixson rank of the free commutative ring on n generators is omega^n, where omega is the smallest infinite ordinal. More generally, we work in the space of finitely generated modules over a given commutative ring.

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