The Tracial Topological Rank of Extensions of $$C^*$$ C ∗ -Algebras

Abstract

Let 0 − → J − → A − → B − → 0 be an extension of C * -algebras. Suppose that both J and B have tracial rank no more than one. It is shown that A has tracial topological rank no more than one whenever it is a quasidiagonal extension, and A has property (P 1 ) if the extension is tracially quasidiagonal.