Noetherian property of subrings of power series rings II
SCIE
SCOPUS
- Title
- Noetherian property of subrings of power series rings II
- Authors
- Kang, BG; Toan, PT
- Date Issued
- 2015-09
- Publisher
- ELSEVIER SCIENCE BV
- Abstract
- Let R be a commutative ring with unit. We study certain subrings R[X; Y, lambda] of R[X][[Y] = R[X-1, ..., X-n][[Y-1, ...,Y-m,]] where A is a nonnegative real-valued increasing function. These subrings naturally arise from studying p-adic analytic variation of zeta functions over finite fields. In our previous work, we gave a necessary and sufficient condition for R[X; Y, lambda] to be Noetherian when Y has more than one variable and lambda grows as fast as linear. In this paper, we show that the same result holds even when Y has only one variable. This contradicts Davis and Wan's result stating that R[X; Y, lambda] is always Noetherian if R is a field. We however found a mistake in their proof. (C) 2015 Elsevier B.V. All rights reserved.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/26988
- DOI
- 10.1016/J.JPAA.2015.02.006
- ISSN
- 0022-4049
- Article Type
- Article
- Citation
- JOURNAL OF PURE AND APPLIED ALGEBRA, vol. 219, no. 9, page. 4055 - 4060, 2015-09
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