Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-29T09:05:29.365Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Open Questions on Minimal Primes of a Krull Domain

Published online by Cambridge University Press:  20 November 2018

Paul M. Eakin Jr.  and
William J. Heinzer
Paul M. Eakin Jr.
Affiliation:
Louisiana State University, Baton Rouge, Louisiana
William J. Heinzer
Affiliation:
Louisiana State University, Baton Rouge, Louisiana
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.

Let A be an integral domain and K its quotient field. A is called a Krull domain if there is a set {Vα} of rank one discrete valuation rings such that A = ∩αVα and such that each non-zero element of A is a non-unit in only finitely many of the Vα. The structure of these rings was first investigated by Krull, who called them endliche discrete Hauptordungen (4 or 5, p. 104).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1261 - 1264
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Bourbaki, N., Eléments de mathématique, algèbre commutative, Chapitre VII (Hermann, Paris, 1965).Google Scholar
2. Cohen, I. S., Commutative rings with restricted minimum condition, Duke Math. J. 17 (1950), 27–42.Google Scholar
3. Eakin, P., The converse to a well-known theorem on noetherian rings (to appear in Math. Ann.).Google Scholar
4. Krull, W., Uber die Zerlegung der Hauptideale in allgemeinen Ringen, Math. Ann. 105 (1931), 1–14.Google Scholar
5. Krull, W., Idealtheorie (Chelsea, New York, 1948).Google Scholar
6. Nagata, M., Local rings (Interscience, New York, 1962).Google Scholar
7. Samuel, P., Lectures on unique factorization domains (Tata Institute, Bombay, 1964).Google Scholar
8. Zariski, O. and Samuel, P., Commutative algebra, Vol. II (Van Nostrand, New York, 1960).10.1007/978-3-662-29244-0CrossRefGoogle Scholar