Firouzabad Institute of Higher EducationAnnals of Optimization Theory and Practice2588-36663120201001Strong algebrability of C^* algebras152411891810.22121/aotp.2020.230247.1029ENJavadSharafiUniversity of Imam AliJournal Article20200507In this paper, we introduce the concept strong algebrability of certain C^* algebras generated by finite generators. In fact, using Gelfand theorem, we identify the members of the C^* algebra generated by one element, with the continuous functions on its spectrum, and use some recent result for strong algebrability for functions spaces.<br /> Moreover, we introduce the new concept unitable elements in unital C^* algebras, and then we express our main result for this kind of elements. In fact, the C^* subalgebra generated by a non unitable element in a C^* algebra is strongly c algebrable.<br /> As the last result in this paper, we show 2^c strong algebrability of direct sums of C^* algebras, using non unitable elements of them.http://aotp.fabad-ihe.ac.ir/article_118918_8ae966989526ff6db6c69d6850e3bd53.pdf