A going-up theorem for arbitrary chains of prime ideals

DOI10.1080/00927879908826671zbMath0969.13004OpenAlexW2131125557MaRDI QIDQ4261262

David E. Dobbs

Publication date: 27 September 2001

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

Full work available at URL: https://doi.org/10.1080/00927879908826671

zbMATH Keywords

going-uplinearly ordered chain of prime ideals

Mathematics Subject Classification ID

Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (7)

Lifting up a tree of prime ideals to a going-up extension. ⋮ Lifting trees of prime ideals to bezout extension domains ⋮ Corrigendum: a going-up theorem for arbitrary chains of prime ideals ⋮ Lifting chains of prime ideals to paravaluation rings ⋮ Going-down implies generalized going-down ⋮ Extensions of commutative rings in which trees of prime ideals contract to trees ⋮ On chain morphisms of commutative rings

Cites Work

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• Kronecker function rings and abstract Riemann surfaces
• Abstract Riemann surfaces of integral domains and spectral spaces
• Lifting up an infinite chain of prime ideals to a valuation ring

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