Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T05:51:05.814Z Has data issue: false hasContentIssue false
  • English
  • Français

The Complete Quotient Ring of Images of Semilocal Prüfer Domains

Published online by Cambridge University Press:  20 November 2018

John Chuchel  and
Norman Eggert
John Chuchel
Affiliation:
Eastern Montana College, Billings, Montana
Norman Eggert
Affiliation:
Montana State University, Bozeman, Montana
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.

It is well known that the complete quotient ring of a Noetherian ring coincides with its classical quotient ring, as shown in Akiba [1]. But in general, the structure of the complete quotient ring of a given ring is largely unknown. This paper investigates the structure of the complete quotient ring of certain Prüfer rings. Boisen and Larsen [2] considered conditions under which a Prüfer ring is a homomorphic image of a Prüfer domain and the properties inherited from the domain. We restrict our investigation primarily to homomorphic images of semilocal Prüfer domains. We characterize the complete quotient ring of a semilocal Prüfer domain in terms of complete quotient rings of local rings and a completion of a topological ring.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 914 - 927
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Akiba, T., Remarks on generalized rings of quotients, III, J. Math., Kyoto Univ. 9-2 (1969), 205–212.Google Scholar
2. Boisen, M. and Larsen, M., On Priifer rings as images of Prilfer domains, Proc. Amer. Math. Soc. 40 (1973), 87–90.Google Scholar
3. Bourbaki, N., Commutative algebra (Addison-Wesley, Reading, Mass., 1972).Google Scholar
4. Bourbaki, N. General topology (Addison-Wesley, Reading, Mass., 1966).Google Scholar
5. Gilmer, R., Multiplicative ideal theory (Marcel Dekker, New York, 1972).Google Scholar
6. Lambek, J., Lectures on rings and modules (Blaisdell, Waltham, Mass., 1966).Google Scholar
7. Larsen, M. and McCarthy, P., Multiplicative theory of ideals (Academic Press, New York, 1971).Google Scholar