Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T20:20:19.163Z Has data issue: false hasContentIssue false
  • English
  • Français

Valuation Rings and Integral Closure

Published online by Cambridge University Press:  20 November 2018

Thomas G. Lucas
Thomas G. Lucas*
Affiliation:
Department of Mathematics University of North Carolina at Charlotte, Charlotte, NC 28223
Rights & Permissions [Opens in a new window]

Abstract

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.

A famous theorem of Krull's is that the integral closure of an integral domain D is the intersection of the valuation domains that contain D. An example is given to show that the same result need not hold for the integral closure of a ring with zero divisors.

Keywords

13A1813B20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 327 - 330
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Gräter, J., Integral closure and valuation rings with zero-divisors, Studia Sci. Math. Hung. 17 (1982), 457–458.Google Scholar
2. Griffin, M., Generalizing valuations to commutative rings, Queen's Math. Preprint No. 1970-40, Queen's Univ., Kingston, Canada, 1970.Google Scholar
3. Griffin, M., Prufer rings with zero divisors, J. reine angew. Math. 239/240 (1970), 55–67.Google Scholar
4. Huckaba, J., On valuation rings that contain zero divisors, Proc. Amer. Math. Soc. 40 (1973), 9–15.Google Scholar
5. Huckaba, J., Commutative rings with Zero Divisors, Dekker, 1988.Google Scholar
6. Krull, W., Allgeneine Beweriungstheorie, J. reine angew. Math. 167 (1932), pp. 160–196.Google Scholar
7. Marot, J., Extension de la notion d'anneau valuation, Dept. Math. Faculté des Sci. de Brest (1968), 46 pp. et 39 pp. de complements.Google Scholar
8. Samuel, P., La notion de place dans un anneau, Bull. Soc. Math. France 85 (1957), 123–133.Google Scholar