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Search: MSC category 06F05 ( Ordered semigroups and monoids [See also 20Mxx] )

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1. CJM 2017 (vol 70 pp. 26)

Bosa, Joan; Petzka, Henning
Comparison Properties of the Cuntz semigroup and applications to C*-algebras
We study comparison properties in the category $\mathrm{Cu}$ aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the CFP and $\omega$-comparison. We show differences of all properties by providing examples, which suggest that the corona factorization for C*-algebras might allow for both finite and infinite projections. In addition, we show that R{\o}rdam's simple, nuclear C*-algebra with a finite and an infinite projection does not have the CFP.

Keywords:classification of C*-algebras, cuntz semigroup
Categories:46L35, 06F05, 46L05, 19K14

2. CJM 2001 (vol 53 pp. 592)

Perera, Francesc
Ideal Structure of Multiplier Algebras of Simple $C^*$-algebras With Real Rank Zero
We give a description of the monoid of Murray-von Neumann equivalence classes of projections for multiplier algebras of a wide class of $\sigma$-unital simple $C^\ast$-algebras $A$ with real rank zero and stable rank one. The lattice of ideals of this monoid, which is known to be crucial for understanding the ideal structure of the multiplier algebra $\mul$, is therefore analyzed. In important cases it is shown that, if $A$ has finite scale then the quotient of $\mul$ modulo any closed ideal $I$ that properly contains $A$ has stable rank one. The intricacy of the ideal structure of $\mul$ is reflected in the fact that $\mul$ can have uncountably many different quotients, each one having uncountably many closed ideals forming a chain with respect to inclusion.

Keywords:$C^\ast$-algebra, multiplier algebra, real rank zero, stable rank, refinement monoid
Categories:46L05, 46L80, 06F05

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