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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-Żelazko conjecture.
David P. Blecher, and Tomasz Kania. "Finite generation in C*-algebras and Hilbert C*-modules." Studia Mathematica 224.2 (2014): 143-151. <http://eudml.org/doc/285484>.
@article{DavidP2014, abstract = {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-Żelazko conjecture.}, author = {David P. Blecher, Tomasz Kania}, journal = {Studia Mathematica}, keywords = {Hilbert module; -module; finitely generated ideal; algebraically finitely generated; maximal ideal; -algebra; Dales-Żelazko conjecture}, language = {eng}, number = {2}, pages = {143-151}, title = {Finite generation in C*-algebras and Hilbert C*-modules}, url = {http://eudml.org/doc/285484}, volume = {224}, year = {2014}, }
TY - JOUR AU - David P. Blecher AU - Tomasz Kania TI - Finite generation in C*-algebras and Hilbert C*-modules JO - Studia Mathematica PY - 2014 VL - 224 IS - 2 SP - 143 EP - 151 AB - 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-Żelazko conjecture. LA - eng KW - Hilbert module; -module; finitely generated ideal; algebraically finitely generated; maximal ideal; -algebra; Dales-Żelazko conjecture UR - http://eudml.org/doc/285484 ER -