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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
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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

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