Affine representations of Grothendieck groups and applications to Rickart 𝐶*-algebras and ℵ₀-continuous regular rings

DOI10.1090/memo/0234zbMath0435.16005OpenAlexW1991111896MaRDI QIDQ3874349

John W. Lawrence, David E. Handelman, Kenneth R. Goodearl

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1090/memo/0234

zbMATH Keywords

Grothendieck groupunit-regular ring*-regular ringscontinuous regular ringspartially ordered Abelian groupscountable interpolation propertyfinite Rickart C*-algebras

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) General theory of von Neumann algebras (46L10) General theory of (C^*)-algebras (46L05) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (25)

On \(\aleph _ 0\)-injective regular rings ⋮ Aleph-nought-continuous regular rings ⋮ Locally semisimple algebras. Combinatorial theory and the \(K_ 0\)- functor ⋮ Spectral resolution in a Rickart comgroup ⋮ Stone duality for Dedekind \(\sigma\)-complete \(\ell\)-groups with order-unit ⋮ Hahn-Banach theorems for MV-algebras ⋮ Transition to effect algebras ⋮ Test groups and effect algebras ⋮ Left and right projections are equivalent in Rickart \(C^*\)-algebras ⋮ State spaces of \(K_ 0\) of Noetherian rings ⋮ The N*-metric completion of regular rings ⋮ Metrically Complete Regular Rings ⋮ Associative rings ⋮ A classification of finite rank dimension groups by their representations in ordered real vector spaces ⋮ Rickart C* algebras. II ⋮ Hulls of semiprime rings with applications to \(C^*\)-algebras. ⋮ Boolean Algebras, Generalized Abelian Rings, and Grothendieck Groups ⋮ \(K_0\)-like constructions for almost completely decomposable groups ⋮ A compactness property of Dedekind \(\sigma\)-complete \(f\)-rings ⋮ Partially ordered Baer involutive algebras ⋮ Von Neumann regular rings: connections with functional analysis ⋮ AF-algebras with lattice-ordered \(K_0\): logic and computation ⋮ Dimension functions and traces on C*-algebras ⋮ On regular rings with involution ⋮ On the \(N^ *\)-metric completion of regular rings

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