Lifting up a tree of prime ideals to a going-up extension.

DOI10.1016/S0022-4049(02)00301-8zbMath1069.13009OpenAlexW2087958404MaRDI QIDQ1399145

Dong Yeol Oh, Byung Gyun Kang

Publication date: 30 July 2003

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

Full work available at URL: https://doi.org/10.1016/s0022-4049(02)00301-8

zbMATH Keywords

spectrumBézout domainintegral extensiongoing-upPrufer domaintree of prime ideals

Mathematics Subject Classification ID

Partial orders, general (06A06) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items

Maximal covers of chains of prime ideals, Going-down implies generalized going-down, On chain morphisms of commutative rings

Cites Work

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• Kronecker function rings and abstract Riemann surfaces
• Going down
• The spectrum of a ring as a partially ordered set
• A going-up theorem for arbitrary chains of prime ideals
• Lifting up an infinite chain of prime ideals to a valuation ring
• Lifting trees of prime ideals to bezout extension domains
• Corrigendum: a going-up theorem for arbitrary chains of prime ideals
• Prime Ideal Structure in Commutative Rings
• Going Down in Polynomial Rings
• On Going Down in Polynomial Rings