The order bidual of f-algebras

In this thesis investigating properties of Riesz algebras and, in particular the properties of f-algebras, which is one of the most important classes, we give a necessary and sufficient condition for the characterization of order bidual with identity element of an Archimedean f-algebra. The thesis mainly consists of four sections: In the first section, giving main definitions and theorems, properties of Riesz spaces and some operators defined on Riesz spaces are investigated. The second section deals with Riesz algebras, their properties and some important classes of Riesz algebras. We investigate the relationships among these classes. In particular, the class of f-algebra is studied in details. We see that the order bidual of an Archimedean f-algebra is an f-algebra (with respect to Arens multiplication), due to (Huijsmans ve Bernau, 1995). In the third section, studying a paper of K. Boulabiar and J. Jaber publihsed in 2011 (Boulabiar ve Jaber, 2011) we get the characterization of order bidual with identity element of an Archimedean f-algebra.