Ali Asghar Estaji - Department of Mathematics, Shahrood University of Technology, Shahrood, Iran.
Ebrahim Hashemi - Department of Mathematics, Shahrood University of Technology
Ali Akbar Estaji - Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.

For a frame L, consider the f-ring \mathcal{F}_{\mathcal P}L=Frm(\mathcal{P}(\mathbb R), L). In this paper, first we show that each minimal ideal of \mathcal{F}_{\mathcal P}L is a principal ideal generated by f_a, where a is an atom of L. Then we show that if L is an \mathcal{F}_{\mathcal P}-completely regular frame, then the socle of \mathcal{F}_{\mathcal P}L consists of those f for which coz (f) is a join of finitely many atoms.  Also it is shown that not only \mathcal{F}_{\mathcal P}L has Property (A) but also if L has a finite number of atoms then the residue class ring \mathcal{F}_{\mathcal P}L/\mathrm{Soc}( \mathcal{F}_{\mathcal P}L) has Property (A).

Minimal ideal, Socle, real-valued functions ring, ring with property (A)