Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T01:04:17.316Z Has data issue: false hasContentIssue false
  • English
  • Français

Local Minimal Overrings

Published online by Cambridge University Press:  20 November 2018

Ira J. Papick
Ira J. Papick*
Affiliation:
Adelphi University, Garden City, New York
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 R be a (commutative integral) domain having quotient field K. A domain S satisfying , is called an overring of R. We say R has a minimal overring T, in case and there are no domains properly between R and T. The purpose of this paper is the study of certain classes of coherent domains having local minimal overrings; that is, having minimal overrings with unique maximal ideals.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 4 , 01 August 1976 , pp. 788 - 792
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Bourbaki, N., Commutative algebra (Addison-Wesley, Reading, Massachusetts, 1972).Google Scholar
2. Dobbs, D. E. and Papick, I. J., When is D + M coherent!, to appear, Proc. Amer. Math. Soc.Google Scholar
3. Eerrand, D. et Olivier, J. P., Homomorphismes minimaux d'amieaux, J. of Algebra 10 (1970), 461–471.Google Scholar
4. Gilmer, R. and \Y. Heinzer, J., Intersections of quotient rings of an integral domain, J. Math. Kyoto University 7-2 (1967), 133–100.Google Scholar
5. Gilmer, R., Multiplicative ideal theory, Queen's Papers in Pure and Appl. Math., No. 12, Queen's University, Kingston, Ontario, 1968.Google Scholar
6. Greenberg, B., Global dimension of Cartesian squares, J. of Algebra 32 (1974), 31–43.Google Scholar
7. Kaplansky, I., Commutative rings (Allyn and Bacon, Boston, Massachusetts, 1970).Google Scholar
8. Matsumura, H., Commutative algebra (\V. A. Benjamin, New York, 1970).Google Scholar
9. Papick, I . J ., Topologically defined classes of going-down domains, to appear, Trans. Amer. Math. Soc.Google Scholar
10. Richman, E., Generalized quotient rings, Proc. Amer. Math. Soc. 16 (1965), 794–799.Google Scholar
11. Vasconcelos, V. V., Divisor theory in module categories, Mathematics Studies No. 14 (North- Holland, Amsterdam, 1974).Google Scholar