The space of finitely generated rings

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.

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

References in corpus (1)

• On the isolated points in the space of groups

Cited by in corpus (1)

• Counting submodules of a module over a noetherian commutative ring