Krull dimension of mixed extensions
SCIE
SCOPUS
- Title
- Krull dimension of mixed extensions
- Authors
- Kang, BG; Park, MH
- Date Issued
- 2009-10
- Publisher
- ELSEVIER SCIENCE BV
- Abstract
- For a commutative ring R with identity, dim R shall stand for the Krull dimension of R. It is known that dim R vertical bar x vertical bar <= 2 dim R + 1. We show that this does not hold for the power series extensions. Using mixed extensions, we construct ail example of a finite-dimensional integral domain R such that 2 dim R + 1 < dimR parallel to x parallel to < infinity. Let D be a finite-dimensional SFT prufer domain and D vertical bar x(1)parallel to...vertical bar x(n)parallel to be a mixed extension. According to Arnold, dim D vertical bar x(1).....x(n)vertical bar = dim D + n and dim D parallel to x(1).....x(n)parallel to = n dim D + 1. We generalize Arnold's result by showing that dim D vertical bar x(1)parallel to...vertical bar x(n)vertical bar = n dim D + 1 provided that there is at least one power series extension. In particular if R = D vertical bar x(1),.... x(n-1)vertical bar and dim D = d > 2(n - 1)/(n - 2), then dim R parallel to x parallel to = dn + 1 > 2 dim R + 1. This is all answer to the question of Coykendall and Gilmer. (C) 2009 Elsevier B.V. All rights reserved
- Keywords
- POWER-SERIES RINGS; PRUFER DOMAINS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/27943
- DOI
- 10.1016/j.jpaa.2009.02.010
- ISSN
- 0022-4049
- Article Type
- Article
- Citation
- JOURNAL OF PURE AND APPLIED ALGEBRA, vol. 213, no. 10, page. 1911 - 1915, 2009-10
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