The completion of Prüfer domains

Močkoř, Jǐŕı

doi:10.1090/s0002-9939-1977-0453727-7

Proc. Amer. Math. Soc.

1977

DOI: 10.1090/s0002-9939-1977-0453727-7

|View full text |Cite

The completion of Prüfer domains

Jǐŕı Močkoř¹

Abstract: Abstract. The completion of Prüfer and almost Dedekind domains in topologies sup{5",: w G fi}, where 5", is a topology induced by a valuation w e fi, are characterized in terms of Manis valuations.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1999

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

On Mockor's Question

Kang

Park

1999

Journal of Algebra

View full text Add to dashboard Cite

For certain classes of Priifer domains A, we study the completion A'~-of A with respect to the supremum topology3= sup{~lw ~ ~/, where l~ is the family of nontrivial valuations on the quotient field which are nonnegative on A and ~ is a topology induced by a valuation w ~ IL It is shown that the concepts "SFT Priifer domain" and "generalized Dedekind domain" are the same. We show that if E is the ring of entire functions, then E'J is a Bezout ring which is not a ff:-PriJfer ring, and if A is an SFT Priifer domain, then .~.3-is a Priifer ring under a certain condition. We also show that under the same conditions as above, ~,9" is a ff:-PriJfer ring if and only if the number of independent valuation overrings of A is finite. In particular, if A is a Dedekind domain (resp., h-local Priifer domain), then 3-A' is a J--Priifer ring if and only if A has only finitely many prime ideals (resp., maximal ideals). These provide an answer to Mockor's question.

show abstract

On Mockor's Question

Kang

Park

1999

Journal of Algebra

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

The completion of Prüfer domains

Abstract: Abstract. The completion of Prüfer and almost Dedekind domains in topologies sup{5",: w G fi}, where 5", is a topology induced by a valuation w e fi, are characterized in terms of Manis valuations.

Cited by 1 publication

References 9 publications

On Mockor's Question

On Mockor's Question

Contact Info

Product

Resources

About