Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-03T19:49:40.175Z Has data issue: false hasContentIssue false
  • English
  • Français

On the flat overrings of an integral domain

Published online by Cambridge University Press:  18 May 2009

Bronislaw Wajnryb  and
Abraham Zaks
Bronislaw Wajnryb
Affiliation:
Technion—I.I.T., Haifa, Israel
Abraham Zaks
Affiliation:
Northwestern University, Evanston, Illinois, U.S.A.
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.

The present paper deals with relations between flat overrings and quotient rings. Weare mainly concerned with Richman's results [10] on flat overrings and withthose of Davis [2], Gilmer [3], Gilmer and Heinzer [4], Gilmer and Ohm [5], and Mott [8], on rings with the QR propertyand with the property (#) defined in Section 1. Some of their results are generalized, and it is shown that certain theorems, which at first glance seem to have nothing in common, are in fact particular cases of a single more general theorem.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 12 , Issue 2 , September 1971 , pp. 162 - 165
Copyright
Copyright © Glasgow Mathematical Journal Trust 1971

References

REFERENCES

1.Cartan, H. and Eilenberg, S., Homological algebra (Princeton, New Jersey, 1956).Google Scholar
2.David, E. D., Overrings of commutative rings II, Trans. Amer. Math. Soc. 110 (1964), 196–212.Google Scholar
3.Gilmer, R., Overrings of Prüfer domains, J. Algebra 4 (1966), 331–340.CrossRefGoogle Scholar
4.Gilmer, R. and Heinzer, W. J., Overrings of Prüfer domains II, J. Algebra 7 (1967), 281–302.CrossRefGoogle Scholar
5.Gilmer, R. and Ohm, J., Integral domains with quotient overrings, Math. Ann. 153 (1964), 813–818.CrossRefGoogle Scholar
6.Goldman, O., On a special class of Dedekind domains, Topology 3, Suppl. 1 (1964), 113–118.CrossRefGoogle Scholar
7.McCoy, N. H., A note on finite unions of ideals and sub-groups, Proc. Amer. Math. Soc. 8 (1957).CrossRefGoogle Scholar
8.Mott, J. L., Integral domains with quotient overrings, Math. Ann. 166 (1966), 229–232.CrossRefGoogle Scholar
9.Pendleton, R., A characterization of Q-domains, Bull. Amer. Math. Soc. 72 (1966), 499–500.CrossRefGoogle Scholar
10.Richman, F., Generalized quotient rings, Proc. Amer. Math. Soc. 16 (1965), 794–799.CrossRefGoogle Scholar
11.Samuel, P., Lectures on unique factorization domains (Tata Institute, Bombay, 1964).Google Scholar
12.Zariski, O. and Samuel, P., Commutative algebra, vols. I and II (Princeton, 1958).Google Scholar