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Two theorems on excellent rings 1)

Published online by Cambridge University Press:  22 January 2016

Silvio Greco
Affiliation:
Istituto Matematico del Politecnico di Torino
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Extract

Let f: A → B be a homomorphism of commutative noetherian rings. The main results of this paper are:

(a) Assume f is finite and induces a surjective map on the spectra. Then if B is quasi-excellent A is quasi-excellent and is excellent if it is universally catenarian (Th. 3.1); and

(b) If f is absolutely flat and A is excellent then B is excellent (Th. 5.3). In particular the strict henselization of an excellent local ring is excellent (Cor. 5.6.).

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

Footnotes

1)

This research was supported by CNR.

References

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