Equivalence of real rank zero in l^∞(A)/J_A with tracial almost divisibility and related properties, plus hyperfiniteness and real rank zero for tracial completions of stable rank one AH-algebras implying tracial strict comparison.
The real and stable rank of tracially complete C*-algebras
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abstract
We prove that a factorial tracially complete C*-algebra with CPoU has real rank zero and stable rank one. This leads to an essentially complete description of the Cuntz semigroup of these algebras. In particular, the results of this paper hold for the uniform tracial completions of $\mathcal{Z}$-stable C*-algebras.
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math.OA 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Divisibility and Real Rank Zero
Equivalence of real rank zero in l^∞(A)/J_A with tracial almost divisibility and related properties, plus hyperfiniteness and real rank zero for tracial completions of stable rank one AH-algebras implying tracial strict comparison.