Finite generation in $C^\ast$-algebras and Hilbert $C^\ast$-modules
  We characterize $C^*$-algebras and $C^*$-modules such that every maximal right ideal (resp. right submodule) is algebraically finitely generated. In particular, $C^*$-algebras satisfy the Dales--\.Zelazko conjecture. 
David P. Blecher and Tomasz Kania
math.OA math.FA