Abstract
Lin and Su classified A\( \mathcal{T} \)-algebras of real rank zero. This class includes all A\( \mathbb{T} \)-algebras of real rank zero as well as many C*-algebras which are not stably finite. An A\( \mathcal{T} \)-algebra often becomes an extension of an A\( \mathbb{T} \)-algebra by an AF-algebra. In this paper, we show that there is an essential extension of an A\( \mathbb{T} \)-algebra by an AF-algebra which is not an A\( \mathcal{T} \)-algebra. We describe a characterization of an extension E of an A\( \mathbb{T} \)-algebra by an AF-algebra if E is an A\( \mathcal{T} \)-algebra.
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Yao, H. A\(\mathcal{T}\)-algebras and extensions of A\(\mathbb{T}\)-algebras. Proc Math Sci 120, 199–207 (2010). https://doi.org/10.1007/s12044-010-0019-y
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DOI: https://doi.org/10.1007/s12044-010-0019-y