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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-3-1, author = {Raymond Mortini}, title = {Embedding polydisk algebras into the disk algebra and an application to stable ranks}, journal = {Annales Polonici Mathematici}, volume = {111}, year = {2014}, pages = {217-221}, zbl = {1328.46041}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-3-1} }
Raymond Mortini. Embedding polydisk algebras into the disk algebra and an application to stable ranks. Annales Polonici Mathematici, Tome 111 (2014) pp. 217-221. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-3-1/