Krull-dimension of the power series ring over a nondiscrete valuation domain is uncountable

Byung Gyun Kang, Mingyu Park

Type: Article

Publication Date: 2013-01-08

Citations: 14

DOI: https://doi.org/10.1016/j.jalgebra.2012.05.017

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Locations

Journal of Algebra - View

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+	Krull dimension of a power series ring over a valuation domain	2018	Phan Thanh Toàn Byung Gyun Kang
+	How to Construct Huge Chains of Prime Ideals in Power Series Rings	2014	Byung Gyun Kang Phan Thanh Toàn
+	Power series over integral domains of Krull type	2022	Le Thi Ngoc Giau Phan Thanh Toàn
+	An infinite cardinal-valued Krull dimension for rings	2018	K. Alan Loper Zachary Mesyan Greg Oman
+	The Krull dimension of power series rings over non-SFT rings	2012	Byung Gyun Kang K. Alan Loper Thomas G. Lucas Mingyu Park Phan Thanh Toàn
+	Krull dimension of power series rings	2020	Phan Thanh Toàn Byung Gyun Kang
+	On power series rings over valuation domains	2017	Le Thi Ngoc Giau Phan Thanh Toàn
+	$\mathbf{A}_{\text {inf}}$ has uncountable Krull dimension	2020	Heng Du
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+ PDF Chat	Some strange behaviors of the power series ring R[[X]]	2018	Toan Phan Thanh

Works Cited by This (15)

Action	Title	Year	Authors
+	Multiplicative ideal theory	1968	Robert Gilmer
+	Real and Complex Analysis.	1987	G. A. Garreau Walter Rudin
+ PDF Chat	Lifting up an infinite chain of prime ideals to a valuation ring	1998	Byung Gyun Kang Dong Yeol Oh
+	Completion of a Prüfer domain	1999	Byung Gyun Kang M.H. Park
+	GCD DOMAINS AND POWER SERIES RINGS	2002	M. H. Park D. D. Anderson Byung Gyun Kang
+ PDF Chat	Power series rings over discrete valuation rings	1981	Jimmy T. Arnold
+	Anti-archimedean rings and power series rings	1998	D. D. Anderson Byung Gyun Kang M H. Park
+	A localization of a power series ring over a valuation domain	1999	Byung Gyun Kang M.H. Park
+ PDF Chat	The valuation theory of meromorphic function fields over open Riemann surfaces	1963	Norman L. Alling
+ PDF Chat	Krull dimension in power series rings	1973	Jimmy T. Arnold