English

The space of finitely generated rings

Commutative Algebra 2010-08-04 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0904.4216,
  title  = {The space of finitely generated rings},
  author = {Yves Cornulier},
  journal= {arXiv preprint arXiv:0904.4216},
  year   = {2010}
}

Comments

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

R2 v1 2026-06-21T12:55:30.212Z