2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131891We provide a negative solution to a question of M. Rieffel who asked if the right and left topological stable ranks of a Banach algebra must always agree. Our example is found amongst a class of nest algebras. We show that for many other nest algebras, both the left and right topological stable ranks are infinite. We extend this latter result to Popescu's non-commutative disc algebras and to free semigroup algebras as well.14 pagesOperator Algebras47A35; 47L75; 19B10text