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The space of finitely generated rings. (English) Zbl 1177.13023

The space of marked commutative rings on \(n\) given generators is a compact metrizable space. The author computed 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. In particular he proved that if \(A\) is a finitely generated ring, then its Cantor-Bendixson rank coincides with its reduced length. So more generally, he work in the space of finitely generated modules over a given commutative ring.

MSC:

13C05 Structure, classification theorems for modules and ideals in commutative rings
13E05 Commutative Noetherian rings and modules
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References:

[1] DOI: 10.1016/0022-4049(71)90002-8 · Zbl 0226.13009
[2] DOI: 10.1081/AGB-120022212 · Zbl 1043.03031
[3] DOI: 10.1016/j.jalgebra.2006.02.012 · Zbl 1132.20018
[4] DOI: 10.1016/0022-4049(73)90030-3 · Zbl 0271.13005
[5] DOI: 10.1081/AGB-120004483 · Zbl 1012.16025
[6] DOI: 10.1081/AGB-120023976 · Zbl 1039.16018
[7] DOI: 10.1016/0022-4049(73)90039-X · Zbl 0275.16020
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