A LOCALIZATION OF A POWER SERIES RING OVER A VALUATION DOMAIN
SCIE
SCOPUS
- Title
- A LOCALIZATION OF A POWER SERIES RING OVER A VALUATION DOMAIN
- Authors
- Kang, BG; Park, MH
- Date Issued
- 1999-07-28
- Publisher
- ELSEVIER SCIENCE BV
- Abstract
- Let V be a valuation domain. It is known that V[X-1,...,X-n]v-(0), is an n-dimensional Noetherian UFD if V has a height 1 prime ideal P and P not equal P-2. We show that V[X-1,...,X-n]v-(0) is an it-dimensional Noetherian regular local ring if V does not have a height 1 prime ideal. If V has a height 1 prime ideal that is idempotent, then dim V[X-1,...,X-n]v-(0) = infinity and t-dim V[X-1,..., X-n]v-(0) = infinity. In the process of obtaining the above result, we introduce a product of infinitely many power series. (C) 1999 Elsevier Science B.V. All rights reserved.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/21069
- DOI
- 10.1016/S0022-4049(97)00211-9
- ISSN
- 0022-4049
- Article Type
- Article
- Citation
- JOURNAL OF PURE AND APPLIED ALGEBRA, vol. 140, no. 2, page. 107 - 124, 1999-07-28
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