Baire's category theorem and prime avoidance in complete local rings

DOI10.1007/BF01237858zbMath0546.13002MaRDI QIDQ798373

Rodney Y. Sharp, Peter Vámos

Publication date: 1985

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

gradecomplete metric spacedepthsystem of parametersNoetheriancomplete local ringBaire's category theoremcountable prime avoidance

Mathematics Subject Classification ID

Complete metric spaces (54E50) Baire category, Baire spaces (54E52) Ideals and multiplicative ideal theory in commutative rings (13A15) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Local rings and semilocal rings (13H99) Complete rings, completion (13J10)

Related Items

Ascent of module structures, vanishing of Ext, and extended modules ⋮ Simple modules and their essential extensions for skew polynomial rings ⋮ Extended modules ⋮ Prime avoidance property ⋮ On finite unions of ideals and cosets ⋮ Infinite coverings of ideals by cosets with applications to regular sequences and balanced big Cohen–Macaulay modules ⋮ Topological properties of semigroup primes of a commutative ring ⋮ The Étale locus in complete local rings ⋮ Cardinalities of prime spectra of precompletions ⋮ An avoidance principle with an application to the asymptotic behaviour of graded local cohomology ⋮ On Hilbert-Samuel coefficients of graded local cohomology modules ⋮ Excellent normal local domains and extensions of Krull domains ⋮ Characterization of completions of noncatenary local domains and noncatenary local UFDs ⋮ ON G-TYPE DOMAINS ⋮ Multiplicities of graded components of local cohomology modules ⋮ Prime ideals in ultraproducts of commutative rings ⋮ Bases of ideals and Rees valuation rings ⋮ Some homological properties of complete modules ⋮ An Uncountably Infinite Number of Indecomposable Totally Reflexive Modules ⋮ Comaximizing and splitting primes ⋮ Avoidance and absorbance ⋮ Local cohomology modules with respect to an ideal containing the irrelevant ideal ⋮ Infinite prime avoidance ⋮ On the Integral Degree of Integral Ring Extensions ⋮ Classification of dominant resolving subcategories by moderate functions ⋮ Certain countably generated big Cohen-Macaulay modules are balanced ⋮ Primitivity in skew Laurent polynomial rings and related rings

Cites Work

• A representation theorem for complete local rings
• On the $\mu^i$ in a minimal injective resolution II.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item