Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-15T10:58:26.390Z Has data issue: false hasContentIssue false
  • English
  • Français

Residual Finiteness of Commutative Rings and Schemes

Published online by Cambridge University Press:  20 November 2018

Aron Simis
Aron Simis*
Affiliation:
Queen's University, Kingston, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This work grew out of a preliminary announcement (Notices of the Amer. Math. Soc. 18 (1971)). Here we modify the definition of residual finiteness given in [2]. This allows us, first of all, to consider a broader class of rings which are “essentially” residually finite and, secondly, to extend the notion to schemes. We then show that, for various topologies on the category of schemes, our notion of residual finiteness is local so that all relevant questions appear already at the ring level.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 960 - 972
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bourbaki, N., Algèbre commutative (Hermann, Paris, 1961, 1965).Google Scholar
2. Chew, K. L., and Lawn, S., Residually finite rings, Can. J. Math. 22 (1970), 92–101.Google Scholar
3. Grothendieck, A., Éléments de géométrie algébrique, Publications Mathématiques (IHES).Google Scholar
4. Lazard, D., Les épimorphismes d'anneaux, Séminaire d'Algèbre Commutative Samuel, P., Exposé 4 (Paris, 1968).Google Scholar
5. Matsumura, H., Commutative algebra (Benjamin, W. A., Inc., New York, 1970).Google Scholar
6. Raynaud, M., Anneaux locaux henséliens, Lecture Notes in Mathematics, Springer-Verlag no. 169 (1970).Google Scholar
7. Roby, N., Les épimorphismes d'anneaux, Séminaire d'Algèbre Commutative Samuel, P. Exposé 8 (Paris, 1968).Google Scholar