The Krull dimension of power series rings over almost Dedekind domains

DOI10.1016/j.jalgebra.2015.05.010zbMath1329.13033OpenAlexW358889980WikidataQ112881602 ScholiaQ112881602MaRDI QIDQ2347991

Byung Gyun Kang, Gyu Whan Chang, Phan Thanh Toan

Publication date: 10 June 2015

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2015.05.010

zbMATH Keywords

Krull dimensionBézout domainalmost Dedekind domainPower series ring

Mathematics Subject Classification ID

Integral domains (13G05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Formal power series rings (13F25)

Related Items (15)

Krull dimension of a power series ring over a valuation domain ⋮ On a theorem by Brewer ⋮ On power series rings over valuation domains ⋮ On the generalized Krull property in power series rings ⋮ Kronecker function rings and power series rings ⋮ Power series over integral domains of Krull type ⋮ Krull dimension of power series rings ⋮ Various properties of a general class of integer-valued polynomials ⋮ A Survey on Flatness in Integer-Valued Polynomial Rings ⋮ Rings of very strong finite type ⋮ Krull dimension of power series rings over non-SFT domains ⋮ When \(D((X))\) and \(D\{\{X\}\}\) are Prüfer domains ⋮ Chains of prime ideals in power series rings ⋮ Unnamed Item ⋮ Noetherian extensions of commutative rings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Constructing chains of primes in power series rings
• Krull dimension of mixed extensions
• The SFT property does not imply finite dimension for power series rings.
• The Krull dimension of power series rings over non-SFT rings
• Power series rings over Prüfer domains
• A note on the dimension theory of rings
• Krull Dimension in Power Series Rings

This page was built for publication: The Krull dimension of power series rings over almost Dedekind domains