Extensions of commutative rings in which trees of prime ideals contract to trees

DOI10.1007/BF02844981zbMath1172.13302MaRDI QIDQ2569597

David E. Dobbs

Publication date: 20 October 2005

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Integral dependence in commutative rings; going up, going down (13B21) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Relevant commutative algebra (14A05)

Cites Work

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• Examples of Jaffard domains
• Topologically defined classes of commutative rings
• Going down
• Topologically Defined Classes of Going-Down Domains
• A going-up theorem for arbitrary chains of prime ideals
• Lifting up an infinite chain of prime ideals to a valuation ring
• On Going Down For Simple Overrings II
• On Going-Down for Simple Overrings. III
• Lifting trees of prime ideals to bezout extension domains
• Generalized Quotient Rings
• Prime Ideal Structure in Commutative Rings