The Krull dimension of power series rings over almost Dedekind domains
SCIE
SCOPUS
- Title
- The Krull dimension of power series rings over almost Dedekind domains
- Authors
- Chang, GW; Kang, BG; Toan, PT
- Date Issued
- 2015-09-15
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Abstract
- Let D be an almost Dedekind domain that is not Dedekind, M be a non-invertible maximal ideal of D, X be an indeterminate over D, and D[X] be the power series ring over D. We first construct an example of eta(1)-sets and we then use this eta(1)-set and M to give a simple proof of dim(D[X]) >= 2(aleph 1). We show that ht(M[X]/MD[X]) >= 2(aleph 1) when D has only countably many non-invertible maximal ideals or when M is countably generated. We finally construct a simple example of almost Dedekind domains that are not Dedekind with given cardinal number of non-invertible maximal ideals. (C) 2015 Elsevier Inc. All rights reserved.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/26653
- DOI
- 10.1016/J.JALGEBRA.2015.05.010
- ISSN
- 0021-8693
- Article Type
- Article
- Citation
- JOURNAL OF ALGEBRA, vol. 438, page. 170 - 187, 2015-09-15
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