Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58538120180101On Property (A) and the socle of the $f$-ring $Frm(mathcal{P}(mathbb R), L)$618049786ENAli Asghar EstajiDepartment of Mathematics, Shahrood University of Technology, Shahrood, Iran.Ebrahim HashemiDepartment of Mathematics, Shahrood University of TechnologyAli Akbar EstajiFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.20161212http://cgasa.sbu.ac.ir/article_49786_0a546042fb7220c95d9b4ec558b5f554.pdf