Some properties of 𝒇-algebras with a 𝝈-bounded approximate unit element

In this work, the main properties of Riesz algebras and 𝑓- algebras which are the most important classes of these algebras are investigated and a necessary and sufficient condition for a characterization of 𝑓- algebras with a 𝜎-bounded approximate unit are examined. The study consists of four parts: In first part, given by the basic definitions and theorems, main properties of Riesz spaces and various transformations defined on these spaces, Riesz algebras and the main properties of that and also some important classes are defined and examined. In the second part, based on Jamel Jaber's study entitled "𝑓- algebras with a 𝜎- bounded approximate unit" (Jaber, 2014), especially investigating the class of 𝑓-algebra, which constitutes the basis of the our study, in details, the characteristics of this algebra class with a 𝜎- bounded approximate unit are examined. In the third part of the study, the results obtained in this study were given. In the last part, some proposals were made for 𝑓 -algebras with a 𝜎 -bounded approximate unit element. 2017,