ON MOCKOR'S QUESTION
SCIE
SCOPUS
- Title
- ON MOCKOR'S QUESTION
- Authors
- Kang, BG; Park, MH
- Date Issued
- 1999-06-15
- Publisher
- ACADEMIC PRESS INC
- Abstract
- For certain classes of Prufer domains A, we study the completion (A) over cap'(T) of A with respect to the supremum topology T = sup{T-w\w is an element of Omega}, where Omega is the family of nontrivial valuations on the quotient field which are nonnegative on A and F-w is a topology induced by a valuation w is an element of Omega. It is shown that the concepts "SFT Prufer domain" and "generalized Dedekind domain" are the same. We show that if E is the ring of entire functions, then (E) over cap(,T) is a Bezout ring which is not a (T) over cap-Prufer ring, and if A is an SFT Prufer domain, then (A) over cap(,T) is a Priifer ring under a certain condition. We also show that under the same conditions as above, (A) over cap(,T) is a (T) over cap-Prufer 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 (A) over cap(,T) is a (T) over cap Prufer ring if and only if A has only finitely many prime ideals (resp., maximal ideals). These provide an answer to Mockor's question. (C) 1999 Academic Press.
- Keywords
- POWER-SERIES RINGS; PRUFER DOMAINS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/21081
- DOI
- 10.1006/jabr.1998.7785
- ISSN
- 0021-8693
- Article Type
- Article
- Citation
- JOURNAL OF ALGEBRA, vol. 216, no. 2, page. 481 - 510, 1999-06-15
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