ANTI-ARCHIMEDEAN RINGS AND POWER SERIES RINGS
SCIE
SCOPUS
- Title
- ANTI-ARCHIMEDEAN RINGS AND POWER SERIES RINGS
- Authors
- Anderson, DD; Kang, BG; Park, MH
- Date Issued
- 1998-01
- Publisher
- MARCEL DEKKER INC
- Abstract
- We define an integral domain D to be anti-Archimedean if boolean AND(n=1)(infinity) a(n)D not equal 0 for each 0 not equal a epsilon D. For example, a valuation domain or SFT Prufer domain is anti-Archimedean if and only if it has no height-one prime ideals. A number of constructions and stability results for anti-Archimedean domains are given. We show that D is anti-Archimedean double left right arrow D[X-l,...,X-n](D-(0)) is quasilocal and in this case D[X-l,...,X-n](D-(0)) is actually an n-dimensional regular local ring. We also show that ii D is an SFT Prufer domain, then D[{X-alpha}](lD-(0)) is a Krull domain for any set of indeterminates {X-alpha}.
- Keywords
- anti-Archimedean domain; SFT Prufer domain; regular local ring; Krull domain; power series ring; valuation domain; PRIME IDEALS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/21103
- DOI
- 10.1080/00927879808826338
- ISSN
- 0092-7872
- Article Type
- Article
- Citation
- COMMUNICATIONS IN ALGEBRA, vol. 26, no. 10, page. 3223 - 3238, 1998-01
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