Refinement monoids with weak comparability and applications to regular rings and $C*$-algebras

DOI10.1090/S0002-9939-96-03059-6zbMath0849.16009OpenAlexW1540096369MaRDI QIDQ4875517

Pere Ara, Enrique Pardo Espino

Publication date: 4 November 1996

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-96-03059-6

zbMATH Keywords

finitely generated projective modulesvon Neumann regular ringscancellation theorem\(C^*\)-algebras of real rank zerosimple refinement monoidsweak comparability condition

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) (K)-theory and operator algebras (including cyclic theory) (46L80) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) (K_0) as an ordered group, traces (19K14)

Related Items (17)

Power-substitution,exchange rings and unit II-regularity ⋮ The type semigroup, comparison, and almost finiteness for ample groupoids ⋮ Related comparability over exchange rings ⋮ On von Neumann regular rings with weak comparability. ⋮ The Global Glimm Property ⋮ Von Neumann regular rings satisfying weak comparability. ⋮ Nowhere scattered \(C^{\ast}\)-algebras ⋮ Ideal Structure of Multiplier Algebras of Simple C^*-algebras With Real Rank Zero ⋮ Extension of refinement rings ⋮ The structure of countably generated projective modules over regular rings ⋮ On Von Neumann Regular Rings With Weak Comparability II ⋮ Metric completions of ordered groups and 𝐾₀ of exchange rings ⋮ UNIT-REGULAR RINGS SATISFYING WEAK COMPARABILITY ⋮ AF-embeddings into \(C^*\)-algebras of real rank zero ⋮ Comparability and \(s\)-comparability of modules over exchange rings ⋮ The Corona Factorization Property and refinement monoids ⋮ The comparable structure of exchange rings

Cites Work

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• Dimension functions and traces on C*-algebras
• Simple regular rings satisfying weak comparability
• \(C^*\)-algebras of real rank zero
• Prime ideals and the continuity of derivations on integral domains
• Injective positively ordered monoids. I
• \(K\)-theoretically simple von Neumann regular rings
• On the representation of simple riesz groups
• Metric completions of ordered groups and 𝐾₀ of exchange rings

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