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- W11038682 abstract "A C -algebra has the ideal property if any ideal (closed, two- sided) is generated (as an ideal) by its projections. We prove a theorem which implies, in particular, that an AH algebra (AH stands for approximately homogeneous) stably isomorphic to a C -algebra with the ideal property has the ideal property. It is shown that, for any AH algebra A with the ideal property and slow dimension growth, the projections in M1(A) satisfy the Riesz decomposition and interpolation properties and K0(A) is a Riesz group. We prove a theorem which describes the partially ordered set of all the ideals generated by projections of an AH algebra A; the special case when the projections in M1(A) satisfy the Riesz decomposition property is also considered. This theorem generalizes a result of G.A. Elliott which gives the ideal structure of an AF algebra. We answer — jointly with M. Dadarlat — a question of G.K. Pedersen, constructing extensions of C -algebras with the ideal property which do not have the ideal property." @default.
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- W11038682 date "1998-01-01" @default.
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- W11038682 title "ON THE AH ALGEBRAS WITH THE IDEAL PROPERTY" @default.
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