On certain homological properties of Stein algebras

DOI10.1007/BF02169288zbMath0944.46048OpenAlexW2169814103MaRDI QIDQ1963325

A. Yu. Pirkovskii

Publication date: 25 January 2000

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02169288

zbMATH Keywords

vector bundlesFréchet algebraalgebra of holomorphic functionsglobal homological dimensionStein algebracomplex Stein spaceprojective Fréchet module

Mathematics Subject Classification ID

Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Stein spaces (32E10) General theory of topological algebras (46H05) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18)

Related Items (7)

Non-Archimedean analytic geometry as relative algebraic geometry ⋮ Dagger geometry as Banach algebraic geometry ⋮ Unnamed Item ⋮ Stein domains in Banach algebraic geometry ⋮ Approximate characterizations of projectivity and injectivity for Banach modules ⋮ Homological dimensions of modules of holomorphic functions on submanifolds of Stein manifolds ⋮ Open embeddings and pseudoflat epimorphisms

Cites Work

• Coincidence of the homological dimensions of the Fréchet algebra of smooth functions on a manifold with the dimension of the manifold
• Homology and cohomology for topological algebras
• A general framwork for a multi-operator functional calculus
• Faisceaux algébriques cohérents
• Analytische Faserungen über holomorph-vollständigen Räumen
• Zur Theorie der Steinschen Algebren und Moduln
• Big projective modules are free
• Projective modules over polynomial rings
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