Completions, valuations and ultrapowers of Noetherian domains

DOI10.1016/j.jpaa.2004.09.002zbMath1101.13012OpenAlexW2086033294MaRDI QIDQ1772255

Jay Shapiro, Bruce Olberding, A. Serpil Saydam

Publication date: 18 April 2005

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.2004.09.002

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Ultraproducts and related constructions (03C20) Completion of commutative rings (13B35)

Related Items (5)

Unnamed Item ⋮ Bounds in polynomial rings over Artinian local rings ⋮ Classifying singularities up to analytic extensions of scalars is smooth ⋮ Dimension and singularity theory for local rings of finite embedding dimension ⋮ Prime ideals in ultraproducts of commutative rings

Cites Work

• Topologically defined classes of commutative rings
• Model theory.
• Imbeddability of a commutative ring in a finite-dimensional ring
• Linear equivalence of ideal topologies
• Prime ideals in ultraproducts of commutative rings
• Valuations Associated with Ideals (II)
• Valuations Associated with a Local Ring (II)
• The prime spectrum of an infinite product of copies of Z
• Definability problems for modules and rings
• On the Structure and Ideal Theory of Complete Local Rings
• Discrete valuations centered on local domains
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