COMPLETION OF A GLOBALIZED PSEUDO-VALUATION DOMAIN
SCIE
SCOPUS
- Title
- COMPLETION OF A GLOBALIZED PSEUDO-VALUATION DOMAIN
- Authors
- Kang, BG; Park, MH
- Date Issued
- 2002-01
- Publisher
- UNIV HOUSTON
- Abstract
- Let R be a pseudo-valuation domain with associated valuation domain V and I a nonzero proper ideal of R. Let (R) over cap R (resp., (V) over cap) be the I-adic (resp., IV-adic) completion of R (resp., V). We show that (R) over cap is a pseudo-valuation domain (which may be a field); and that if I not equal I-2, then (V) over cap is the associated valuation domain of (R) over cap. Let R be an SFT globalized pseudo-valuation domain with associated Prufer domain T and I a nonzero proper ideal of R. Let (R) over cap (resp., (T) over cap) be the I-adic (resp., IT-adic) completion of R (resp., T). We also show that (R) over cap is an SFT globalized pseudo-valuation ring with associated Prufer ring (T) over cap; and that (R) over cap is an SFT globalized pseudo-valuation domain if and only if rootI is a prime ideal.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29835
- ISSN
- 0362-1588
- Article Type
- Article
- Citation
- HOUSTON JOURNAL OF MATHEMATICS, vol. 28, no. 4, page. 701 - 710, 2002-01
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