The stable range of  C*-algebras.

Richard H. Herman; L.N. Vaserstein

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Generalized canonical algebras and standard stable tubes

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We introduce a new wide class of finite-dimensional algebras which admit families of standard stable tubes (in the sense of Ringel [17]). In particular, we prove that there are many algebras of arbitrary nonzero (finite or infinite) global dimension whose Auslander-Reiten quivers admit faithful standard stable tubes.

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Stability of $C^{*}$ -algebras is not a stable property.

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Embedding polydisk algebras into the disk algebra and an application to stable ranks

Raymond Mortini (2014)

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It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra A(𝔻̅). As a consequence, one obtains uniform closed subalgebras of A(𝔻̅) which have arbitrarily prescribed stable ranks.