The Krull dimension of power series rings over non-SFT rings

DOI10.1016/j.jpaa.2012.06.006zbMath1276.13004OpenAlexW2007574097WikidataQ112882000 ScholiaQ112882000MaRDI QIDQ1946166

Mi Hee Park, Byung Gyun Kang, Thomas G. Lucas, Phan Thanh Toan, K. Alan Loper

Publication date: 18 April 2013

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2012.06.006

zbMATH Keywords

Krull dimensionSFT ringRing of power series

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Formal power series rings (13F25)

Related Items (14)

Nicely-contractible ideals, z0−ideals and z−ideals in formal series rings in finitely many variables ⋮ Krull dimension of a power series ring over a valuation domain ⋮ On a theorem by Brewer ⋮ On power series rings over valuation domains ⋮ Maximal covers of chains of prime ideals ⋮ On the generalized Krull property in power series rings ⋮ How to Construct Huge Chains of Prime Ideals in Power Series Rings ⋮ Power series over integral domains of Krull type ⋮ Krull dimension of power series rings ⋮ Rings of very strong finite type ⋮ Krull dimension of power series rings over non-SFT domains ⋮ Chains of prime ideals in power series rings ⋮ Unnamed Item ⋮ The Krull dimension of power series rings over almost Dedekind domains

Cites Work

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• Krull-dimension of the power series ring over a nondiscrete valuation domain is uncountable
• Constructing chains of primes in power series rings
• Krull dimension of mixed extensions
• A localization of a power series ring over a valuation domain
• The SFT property does not imply finite dimension for power series rings.
• Power series rings over Prüfer domains
• A note on the dimension theory of rings
• FORMAL POWER SERIES RINGS OVER ZERO-DIMENSIONAL SFT-RINGS
• Krull Dimension in Power Series Rings

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