On the generalized Krull property in power series rings
SCIE
SCOPUS
- Title
- On the generalized Krull property in power series rings
- Authors
- Giau L.T.N.; Kang B.G.; Toan P.T.
- Date Issued
- 2020-11
- Publisher
- ELSEVIER
- Abstract
- One open problem in commutative algebra and field arithmetic posed by Jarden is whether the power series ring R[X] is a generalized Krull domain if R is a generalized Krull domain. Assuming R is a generalized Krull domain, Paran and Temkin proved that R[X] is a generalized Krull domain if and only if R[X] is a Krull domain. Hence, if R is a generalized Krull domain that is not a Krull domain, then R[X] is never a generalized Krull domain. In this paper, we show that the assumption R is a generalized Krull domain in Paran and Temkin's result can be dropped. In other words, R[X] is a generalized Krull domain if and only if R[X] is a Krull domain and hence if and only if R is a Krull domain. (C) 2020 Elsevier B.V. All rights reserved.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/105535
- DOI
- 10.1016/j.jpaa.2020.106409
- ISSN
- 0022-4049
- Article Type
- Article
- Citation
- JOURNAL OF PURE AND APPLIED ALGEBRA, vol. 224, no. 11, 2020-11
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